Question

The difference between the local extreme values of the function \(f(x) = 2x^3-15x^2+36x+40\) is ......

• A. \(4\)
• B. \(3\)
• C. \(2\)
• D. \(1\)

Hint:

Find $f'=0$, then compute $f$ at both critical points.

Answer 1

The Correct Option is D

Step 1: Use the sign of the derivative
$f'$ is positive for $x<2$, negative between $2$ and $3$, and positive after $3$. So $x=2$ is a local max and $x=3$ is a local min.

Step 2: Difference
$f(2)-f(3)=(16-60+72)-(54-135+108)=28-27=1$.

Final Answer:
Option (D). \[ \boxed{\text{(D)}} \]