$$\text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. }$$
-$$f ( x ) = 5 x ^ { 2 } , x \geq 0 , a = 3$$
A) 30
B) $\frac { 1 } { 30 }$
C) $\frac { 1 } { 45 }$
D) $\frac { 1 } { 10 }$

Question

Quizplus · Accepted Answer

Given $f(x) = 5x^2$, the derivative $f'(x) = 10x$. At $x = a = 3$, $f'(3) = 10 \cdot 3 = 30$. The derivative of the inverse function at $x = f(a)$ is the reciprocal of the derivative of the function at $a$, so $\frac{df^{-1}}{dx} = \frac{1}{f'(a)} = \frac{1}{30}$.

Find the value of df−1/dx at x=f(a). \text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. } Find the value of df−1/dx at x=f(a).

$\text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. }$