Hi, these are just a few problems from my assignment I am having a hard time with. Any help is appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

1) consider function f(x) = 1/3X^3 - 1/2^2 - 6x + 4

a) find the points on the graph at which the tangent lines are horizontal.

b) find the slope of the line tangent to the curve at x = 3

f) write an equation of this tangent line

2) After t years the population P is given by P(t) = 2000t^2 + 10000t

what is the growth rate at t = 10?

Find the derivative: (I put my answers, please doublecheck, thanks)

a) f(x) = 1/2x^1/2 + 2/3x^1/4 - x^1/5

f'(x) = 1/4x^-1/2 + 1/6x^-3/4 - 1/5x^-4/5

b) y = 5x^1/3

y'= 5/3x^-2/3

c) g(x) = x^1/3 - x^1/3

g'(x) = 1/3x^-2/3 - 1/3x^-2/3

d) y = x^-3/4 - 3x^2/3

y'= -3/4x^-7/4 - 2x^-1/3

e) h(x) = x/2 + 2/x

h'(x) = ?

f) y = (3x^2 - 5x +7)/4

y'= ?

g)f(x) = -1/3x^3 + 4x^2 - 5x + 6

f'(x)= -x^2 + 8x - 5

h) g(x) = (x^3 + x^5)/(x^2)

g'(x) = ?

Thanks again!!

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# Derivative HW

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