If for , find the minimum number of roots of (f'(x))^2 ( f(x))+ ( f(x)) ,f''(x)=0 in…

MATHEMATICS · Numerical · A Level · Mathematics · Differentiation · Differentiation

Problem

If f(x)=(x−a)(x−b)f(x)=(x-a)(x-b) for a,b∈Ra,b\in\mathbb{R}, find the minimum number of roots of π(f′(x))2cos⁡(πf(x))+sin⁡(πf(x)) f′′(x)=0\pi(f'(x))^2\cos(\pi f(x))+\sin(\pi f(x))\,f''(x)=0 in (α,β)(\alpha,\beta), where f(α)=3=f(β)f(\alpha)=3=f(\beta) and α<a<b<β\alpha<a<b<\beta.

Related theory

Browse the problem library