Let f(x)=ax^ 17 +b x 2x 3x+cx^2 ( x)+d (x+ 1+x^2 )+x (|x+1|-|x-1| ) ( e^x-e^ -x…

MATHEMATICS · Numerical · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

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

where

a>0

and

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

. If

f(-7)=7

f(-5)=-5

, and

f(-2)=3

, find the minimum number of zeroes of

f(x)=0