Estimate the derivative of the function $f ( x ) = \frac { x ^ { 2 } } { 8 } - \frac { x ^ { 3 } } { 6 }$ at the point $x = - 2$ .
Please select the correct answer rounded to the nearest hundredth.

A)-2.5
B) -2.55
C) -3
D) -0.5
E) -2.45

Question

Estimate the derivative of the function $f ( x ) = \frac { x ^ { 2 } } { 8 } - \frac { x ^ { 3 } } { 6 }$ at the point $x = - 2$ .  
Please select the correct answer rounded to the nearest hundredth.
 
A)-2.5
B) -2.55
C) -3
D) -0.5
E) -2.45

Quizplus · Accepted Answer

To find the derivative, compute $f'(x) = \frac{d}{dx}(\frac{x^2}{8} - \frac{x^3}{6}) = \frac{x}{4} - \frac{x^2}{2}$. Evaluating at $x = -2$, $f'(-2) = \frac{-2}{4} - \frac{(-2)^2}{2} = -0.5 - 2 = -2.5$.

Estimate the Derivative of the Function f(x)=x28−x36f ( x ) = \frac { x ^ { 2 } } { 8 } - \frac { x ^ { 3 } } { 6 }f(x)=8x2​−6x3​

Estimate the Derivative of the Function $f ( x ) = \frac { x ^ { 2 } } { 8 } - \frac { x ^ { 3 } } { 6 }$