A calculus problem by Rohith M.Athreya

Calculus Level 3

Given a function $f(x)=(60073-x^{10})^{\frac{1}{10}}$ and $f'(2)=\dfrac{1}{f'(a)}$ , where $a$ is a positive integer.

Find $a$ .

2 solutions

Rohith M.Athreya
Jan 12, 2017

Note that $\displaystyle \large f(f(x)) = x$

$\displaystyle \large f^{'}(x)=\frac{1}{f^{'}(f(x))}$

$\displaystyle \large f^{'}(2)=\frac{1}{f^{'}(f(2))}$

$\displaystyle \large f(2)=3=a$

I say this is a lovely sum

Md Zuhair - 4 years, 4 months ago

will add two such questions a day

have fun!!

Rohith M.Athreya - 4 years, 4 months ago

Thanks.. keep adding

Md Zuhair - 4 years, 4 months ago

very nyc problem

rakshith lokesh - 3 years, 2 months ago

Wonderful sum

Sumanth Hegde - 2 years, 8 months ago

I did it the long way, got 59049^(1/10) which simplified to 3. Nice question.

Anurag hooda - 2 years, 5 months ago

J Joseph
Feb 9, 2017

$\left ( f^{-1} \right )'\left ( f\left (x \right ) \right ) = \frac{1}{f'\left(x \right )}$

$\left( f^{-1} \right )'\left( f \left( 3 \right ) \right ) = f'(2)$

$a = 3$