To make a phrase/words, solve the 18 application of derivativesbelow.  Then replace each numbered blank with the lettercorresponding to the answer for that problem. Show allsolutions on the answers given below.

"   __ __ __ __ __ ____       __ __ ____      __ __ __ __ __ ____      __ __ __ ____      __ __ __ ____"       

"__ __ __ __ __ __ __      ____      __      ____ __ __ __ __ __      __ __ __ ____      __ __ __."     

Derivative ApplicationProblems:      

1.  Find the equation of the line normal to thecurve  f(x) = x³ –3x²  at the point (1,-2).          

2.  Find the equation of the line tangent to thecurve  x² y – x = y³ –8  at the point where x =0.          

3.  Determine the point(s) of inflectionof  f(x) = x³ – 5x² + 3x +6.         

4.  Determine the relative minimum point(s)of  f(x) = x⁴ –4x³.        

5.  A particle moves along a line according to the laws = 2t³ – 9t² + 12t – 4, where t?0.  Determine the total distance traveled between t = 0and t =4.             

6.  A particle moves along a line according to the laws = t⁴ – 4t³, wheret?0.    Determine the total distance traveledbetween t = 0 and t =4.        

7.  If one leg, AB, of a right triangle increases atthe rate of  2 inches per second, while theother   leg, AC,  decreases at 3 inchesper second, determine how fast the hypotenuseis   changing (in feet per second) when AB = 6 feetand AC = 8 feet.     

8.  The diameter and height of a paper cup in theshape of a cone are both 4 inches, and water isleaking   out at the rate of ½ cubic inch persecond.  Determine the rate (in inches per second) atwhich  the water level is dropping when the diameter ofthe surface is 2 inches.     

9.  For what value of y is the tangent to thecurve  y² – xy + 9 = 0vertical?        

10.  For what value of  k  is theline  y = 3x + k tangent to the curve  y =x³ ?        

11.  Determine the slopes of the two tangents that canbe drawn from the point (3, 5) to theparabola    y = x².              

12.  Determine the area of the largest rectangle thatcan be drawn with one side along the x-axis and  

two vertices on the curve  y = e^-x2

13.  A tangent drawn to the parabola  y = 4– x²  at the point (1, 3)  forms aright triangle with the   coordinateaxes.  What is the area of thistriangle?         

14.  If the cylinder of largest possible volume isinscribed in a given sphere, determine the ratio ofthe   volume of the sphere to that of thecylinder.

15.  Determine the first quadrant point on thecurve  y²x = 18 which is closest to thepoint  (2, 0).     

16.  Two cars are traveling along perpendicular roads,car A at 40 mph, car B at 60 mph.  At noonwhen   car A reaches the intersection, car B is 90miles away, and moving toward it.  At 1PM, whatis   the rate, in miles per hour, at which thedistance between the cars is changing?