What is the maximum number of possible extreme values for the function, $$ f(x)=x^{3}-7 x-6 $$ ? A. 3 B. 2 c. 1 D. 4

Question

UpStudy AI · Accepted Answer

1. First, compute the derivative of the function:
   $$
   f(x) = x^3 - 7x - 6 \quad\Rightarrow\quad f'(x) = 3x^2 - 7.
   $$

2. Set the derivative equal to zero to find the critical points:
   $$
   3x^2 - 7 = 0.
   $$

3. Solve for $$ x $$:
   $$
   3x^2 = 7 \quad\Rightarrow\quad x^2 = \frac{7}{3} \quad\Rightarrow\quad x = \pm \sqrt{\frac{7}{3}}.
   $$

4. There are two critical points, so the function can have at most two extreme values (one local maximum and one local minimum).

The answer is B. 2.
The function $$ f(x) = x^3 - 7x - 6 $$ has at most 2 extreme values.

What is the maximum number of possible extreme values for the function, \( f(x)=x^{3}-7 x-6 \) ? A. 3 B. 2 c. 1 D. 4