Derrivatives calc

Question

suppose that f(x)=-2x^-4 + 9x^-2

Evaluate each of the following:

f '(2)=

f '(-2)=

Answer 1

For f(x) = -2x^-4 + 9x^-2 using the power rule, f '(x) = (-4)(-2)x^-5 + (-2)(9)x^-3 = 8x^-5 - 18x^-3

So f '(2) = 8(2)^-5 - 18(2)^-3 = 8/2⁵ - 18/2³ = 8/32 - 18/8 = 1/4 - 9/4 = -8/4 = -2

And f '(-2) = 8(-2)^-5 - 18(-2)^-3 = -8/2⁵ + 18/2³ = -8/32 + 18/8 = -1/4 + 9/4 = 8/4 = 2