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this as a whole question 1, answer all parts please a)Show that the derivative of f(x)...

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Basic Math

this as a whole question 1, answer all parts please

a)Show that the derivative of f(x) = 6+4x^2 is f(x)'=8x by usingthe definition of the derivative as the limit of a differencequotient.

b)If the area A = s^2 of an expanding square is increasing atthe constant rate of 4 square inches per second, how fast is thelength s of the sides increasing when the area is 16 squareinches?

c)Find the intervals where the graph of y = x^3-5x^2+2x+4 isconcave up and concave down, and find all the inflectionpoints.

d)Find all the relative maximum and/or relative minimum valuesand points of F(x) = (x^4/3)-2x^2

e)Find all the relative maximum and/or relative minimum valuesand points of F(x)=x^4-4x on the closed interval [0,4]

f)A particle moves along the x-axis with an acceleration givenby a(t)=4t + 7, where t is measured in seconds and s (position) ismeasured in meters. If the initial position is given by s(0) = 4and the initial velocity is given by v(0) = 7 then find theposition of the particle at t seconds.

g)Find the maximum value of xy if it is required that 7x + 1y =62

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