Question

Derive the function f(x) = -2x⁸ - x² at the point (2, 3).

a) 32
b) -32
c) 64
d) -64

Answer 1

The derivative of the function f(x) = -2x⁸ - x² at x = 2 is -2052, which does not match any of the provided options.

Step-by-step explanation:

The question asks us to find the derivative of the function f(x) = -2x⁸ - x² at the point (2, 3). First, we find the derivative f'(x) of the function:

• The derivative of -2x⁸ is -16x⁷.
• The derivative of -x² is -2x.

Thus, the derivative function is f'(x) = -16x⁷ - 2x. Next, we evaluate this derivative at the point where x = 2:

f'(2) = -16(2)⁷ - 2(2)

We calculate:

• -16(2)⁷ = -16 * 128 = -2048
• -2(2) = -4

f'(2) = -2048 - 4 = -2052

However, the options provided (32, -32, 64, -64) do not include -2052. Therefore, there might be a misunderstanding in the question or the options provided.