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

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 using the definition of the derivative as the limit of a difference quotient.

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

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

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

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

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

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

Expert Solution

milcah answered 2 years ago

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