What is $$ f^{\prime}(-8) $$ of $$ f(x)=-3 x^{2}+2 x+4 $$ ?

Question

UpStudy AI · Accepted Answer

To find the derivative $$ f'(x) $$ of the function $$ f(x) = -3x^2 + 2x + 4 $$ and evaluate it at $$ x = -8 $$, follow these steps:

1. **Differentiate $$ f(x) $$:**

$$
   f'(x) = \frac{d}{dx}(-3x^2) + \frac{d}{dx}(2x) + \frac{d}{dx}(4)
   $$
   
   $$
   f'(x) = -6x + 2
   $$

2. **Evaluate $$ f'(x) $$ at $$ x = -8 $$:**

$$
   f'(-8) = -6(-8) + 2
   $$
   
   $$
   f'(-8) = 48 + 2 = 50
   $$

**Answer:** $$ f'(-8) = 50 $$
$$ f'(-8) = 50 $$

What is \( f^{\prime}(-8) \) of \( f(x)=-3 x^{2}+2 x+4 \) ?