If f(t) = $\frac { 1 } { x ^ { 2 / 3 } }$ , then $\lim _ { h \rightarrow 0 }$ $\frac { f ( - 8 + h ) - f ( - 8 ) } { h }$ equals
A) f'(8)
B) $\frac { 1 } { 48 }$
C) f'(0)
D) none of these

Question

Quizplus · Accepted Answer

The given limit represents the definition of the derivative of $f(t)$ at $t = -8$. Calculating the derivative of $f(t) = \frac{1}{x^{2/3}}$ and evaluating it at $t = -8$ gives $\frac{1}{48}$.

If F(t) = 1x2/3\frac { 1 } { x ^ { 2 / 3 } }x2/31​

If F(t) = $\frac { 1 } { x ^ { 2 / 3 } }$