Given the function f (x) = x^2 - 2x^5

Determine the instantaneous rate of change at f at x=4.

Instantaneous rate of change of f (x) at x = 4 is - 2552

Step-by-step explanation:

We have f (x) = x² - 2x⁵

We need to find the instantaneous rate of change of f (x) at x=4

Let us take derivative,

f' (x) = 2x - 10x⁴

Now we need to find f' (4)

Substituting x = 4

We have

f' (4) = 2 x 4 - 10 x 4⁴

f' (4) = 8 - 2560

f' (4) = - 2552

Instantaneous rate of change of f (x) at x = 4 is - 2552