If $$ f(x)=4+3 x-3 x^{2} $$, find $$ f^{\prime}(-5) $$.

Question

UpStudy AI · Accepted Answer

To solve the problem, we first need to find the derivative of the function. The function given is

f(x) = 4 + 3x - 3x².

1. Differentiate term by term:
  - The derivative of 4 is 0.
  - The derivative of 3x is 3.
  - The derivative of -3x² is -6x (using the power rule).

So, the derivative of the function is

f '(x) = 3 - 6x.

2. Now, evaluate the derivative at x = -5:
  f '(-5) = 3 - 6(-5) = 3 + 30 = 33.

Thus, the value of f '(-5) is 33.
$$ f'(-5) = 33 $$

If , find .