Let be defined on the set of real numbers

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)=ax^{17}+b\sin x\sin2x\sin3x+cx^2\sin(\sin x)+d\log(x+\sqrt{1+x^2})+x(|x+1|-|x-1|)\left(\frac{e^x-e^{-x}}{e^x+e^{-x}}\right)

be defined on the set of real numbers, where

a>0

and

b,c,d\in\mathbb{R}

. If

f(-7)=7

f(-5)=-5

, and

f(-2)=3

, then the minimum number of zeroes of

f(x)=0