Question

Find the derivative of F(x)=-x^4+4x^3+ 70 for 0<=x<=3

Answer 1

-4x^3 +12x^2 for 0 < x < 3

Explanation:

The power rule is appropriate:

(d/dx)x^n = n·x^(n-1)

This is applied to each of the terms.

F'(x) = -(4·x^3) +4(3x^2) +0

F'(x) = -4x^3 +12x^2 . . . . for 0 < x < 3

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The derivative is not defined at the endpoints of the interval, so F'(x) is only defined on (0, 3), not [0, 3].