Question

When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is five times the value of f'(3).

Answer 1

hi,

Answer 2

\[f'(a) = 5 f'(3)\]
First you need to know the function f'(x)
\[f'(x) = \frac{d}{dx} \sqrt{x} = \frac{d}{dx} x^{1/2} = \frac{1}{2}x^{-1/2} = \frac{1}{2 \sqrt{x}}\]
\[\frac{1}{2\sqrt{a}}=\frac{5}{2\sqrt{3}}\]

Answer 3

cancel the 2's , then take reciprocal of both sides
\[\sqrt{a} = \frac{\sqrt{3}}{5}\]
\[a = \frac{3}{25}\]