1. You are given the graph of a function f. Determinethe intervals where f is increasing, constant, ordecreasing. (Enter your answers using interval notation. If ananswer does not exist, enter DNE.)

The x y-coordinate plane is given. The curveenters the window in the second quadrant, goes down and rightbecoming less steep, changes direction at the point (?1, 0), goesup and right becoming more steep, passes through the approximatepoint (?0.58, 0.44), goes up and right becoming less steep, changesdirection at the point (0, 1), goes down and right becoming moresteep, passes through the approximate point (0.58, 0.44), goes downand right becoming less steep, changes direction at the point (1,0), goes up and right becoming more steep, and exits the window inthe first quadrant.

increasing=

constant=

decreasing=

2.Solar Panel Power Output

The graph of the function f shown in the accompanyingfigure gives the average "fixed" solar panel power output over a15-hr period on a typical day. Determine the interval(s) wheref is increasing, the interval(s) where f isconstant, and the interval(s) where f is decreasing.Here,

t = 0

corresponds to 5 a.m. (Enter your answers using intervalnotation. If an answer does not exist, enter DNE.)

The t y-coordinate plane is given. Thet-axis is labeled: (hr) and the y-axis islabeled: Solar panel operating capacity (%).

• The curve begins above the t value 0, goes up andright until it reaches the t value 6 and approximatey value of 100.
• The curve continues from the t value 6 horizontallyright until it reaches the t value 9.
• The curve continues from the t value 9 going down andright until it reaches the t value 14 and approximatey value of 5.
• The curve continues from the t value 14 horizontallyright until it reaches the t value 15.

Source: Solarcity.com/California

increasing=

constant=

decreasing=

3.You are given the graph of a function f. Determinethe relative maxima and relative minima, if any. (If an answer doesnot exist, enter DNE.)

The x y-coordinate plane is given. Thefunction enters the window in the second quadrant, goes down andright, changes direction at the point (?4, 0), goes up and rightbecoming less steep, changes direction at the point (0, 16), goesdown and right becoming more steep, changes direction at the point(4, 0), goes up and right, and exits the window in the firstquadrant.

relative minimumsmaller x-value

(x, y)

=

relative minimumlarger x-value

(x, y)

=

(x, y)relative maximum

=

4.You are given the graph of a function f. Determinethe relative maxima and relative minima, if any. (If an answer doesnot exist, enter DNE.)

The x y-coordinate plane is given. The curvewith 3 parts enters the window at in the second quadrant, goes downand right becoming more steep, exits in the third quadrant almostvertically just to the left of x = ?2, reenters in thesecond quadrant almost vertically just to the right of x =?2, goes down and right becoming less steep, changes direction atthe point (0, 4), goes up and right becoming more steep, exitsalmost vertically just to the left of x = 2, reenters inthe fourth quadrant almost vertically just to the right ofx = 2, goes up and right becoming less steep, and exitsthe window in the first quadrant.

relative minimum

(x, y)

=

  (x, y)relative maximum

=

5.Find the x-value(s) of the relative maxima andrelative minima, if any, of the function. (If an answer does notexist, enter DNE.)

f(x) = 1/2x² ? 4x + 1
relative maxima:

x =

relative minima:

x =

6.Find the relative maxima and relative minima, if any, of thefunction. (If an answer does not exist, enter DNE.)

f(x) = x³ ? 12x + 10

relative maximum(x, y)=

relative minimum(x, y)=

7.Find the relative maxima and relative minima, if any, of thefunction. (If an answer does not exist, enter DNE.)

F(t) = 3t⁵ ? 5t³ + 12

relative maximum(x, y)=

relative minimum(x, y)=

8.Find the relative maxima and relative minima, if any, of thefunction. (If an answer does not exist, enter DNE.)

f(x) = X/X+4

relative minimum (x, y)=

relative maximum(x, y)=

9.

You are given the graph of a function f.

The x y-coordinate plane is given. A curve and2 vertical lines are graphed.

• A vertical line crosses the x-axis at x =?4.
• A vertical line crosses the x-axis at x =4.
• The curve with 3 parts enters the window just above thex?axis, goes up and right becoming more steep, exitsalmost vertically just to the left of x = ?4, reentersalmost vertically just to the right of x = ?4, goes up andright becoming less steep, changes direction at the point (0,?0.5), goes down and right becoming more steep, exits almostvertically just to the left of x = 4, reenters almostvertically just to the right of x = 4, goes down and rightbecoming less steep, and exits the window just above thex?axis.

Determine the intervals where the graph of f is concaveupward and where it is concave downward. (Enter your answers usinginterval notation.)

concave upward=

concave downward=

Find the inflection point of f, if any. (If an answerdoes not exist, enter DNE.)

(x, y) =

10.

You are given the graph of a function f.

The x y-coordinate plane is given. The curveenters the window in the second quadrant nearly horizontal, goesdown and right becoming more steep, is nearly vertical at the point(0, 1), goes down and right becoming less steep, crosses thex-axis at approximately x = 1, and exits thewindow just below the x?axis.

Determine the intervals where the graph of f is concaveupward and where it is concave downward. (Enter your answers usinginterval notation.)

concave upward=

concave downward=

Find the inflection point of f. (If an answer does notexist, enter DNE.)

(x, y) =

11.

Refer to the graph of f shown in the followingfigure.

The x y-coordinate plane is given. There is 1curve and 9 dashed lines on the graph.

• The curve starts at the point (0, 1), goes up and rightbecoming more steep, passes through the approximate point (2, 2.4),goes up and right becoming less steep, changes direction at theapproximate point (3, 3), goes down and right becoming more steep,passes through the approximate point (4, 2.2), goes down and rightbecoming less steep, changes direction at the point (5, 1), goes upand right becoming more steep, passes through the point (6, 2),goes up and right becoming almost horizontal at the point (7, 3),goes up and right becoming more steep, changes direction at thepoint (9, 6), goes down and right becoming less steep, and exitsthe window at the point (12, 2).
• The 9 dashed vertical lines extend from the x?axis tothe curve at x = 1, 2, 3, 4, 5, 6, 7, 9, and 12.

(a)

Find the intervals where f is concave upward and theintervals where f is concave downward. (Enter your answersusing interval notation.)

concave upward=

concave downward=

(b)

Find the inflection points of f. (Order your answersfrom smallest to largest x, then from smallest to largesty. If an answer does not exist, enter DNE.)

(x, y)	=
(x, y)	=
(x, y)	=
(x, y)	=

12.

Determine where the function is concave upward and where it isconcave downward. (Enter your answer using interval notation. If ananswer does not exist, enter DNE.)

g(x) = ?x² + 9x + 8

concave upward=

concave downward=

13.

Determine where the function is concave upward and where it isconcave downward. (Enter your answer using interval notation. If ananswer does not exist, enter DNE.)

g(x) =

x ? 4

concave upward=

concave downward=

14.

Determine where the function is concave upward and where it isconcave downward. (Enter your answer using interval notation. If ananswer does not exist, enter DNE.)

g(x) =

x

x + 8

concave upward=

concave downward=

15.

Determine where the function is concave upward and where it isconcave downward. (Enter your answer using interval notation. If ananswer does not exist, enter DNE.)

f(x) =

x + 3

x ? 3

concave upward=

concave downward=

16.

Determine where the function is concave upward and where it isconcave downward. (Enter your answer using interval notation. If ananswer does not exist, enter DNE.)

f(x) = (x ? 3)^2/3

concave upward=

concave downward=

17.

Find the inflection point(s), if any, of the function. (If ananswer does not exist, enter DNE.)

g(x) =4x⁴ ? 8x³+ 1

smaller x-value (x,y)	=
largerx-value (x, y)	=

18.

Find the inflection point, if any, of the function. (If ananswer does not exist, enter DNE.)

f(x) = (x? 8)^4/3

(x, y) =

19. Find the inflection point, if any, of the function. (If ananswer does not exist, enter DNE.) f(x) = 6 + 6 x (x, y) = 20.