Question

if f(x)=x³÷[a²-x²] then f'(a÷2) =?​

Answer 1

Given,

f(x) = ${\dfrac{x^3}{a^2-x^2}$

Now,Given to find,

f(a/2) = ????

Proof :-

Now, SUBSTITUTING a/2 in place of x, we get,

f(a/2) = ${\dfrac{a^2/4}{a^2-a^2/4}}$

-» ${\dfrac{a^2/4}{3a^2/4}}$

-» ${\dfrac{1}{3}}$

Therefore, f(a/2) = ${\dfrac{1}{3}}$