JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 11

Turning points. $f(x)=x^7-7x-2$, $f'(x)=7(x^6-1)=0$ at $x=\pm1$.

Values. $f(-1)=4>0$ and $f(1)=-8<0$, with $f\to-\infty$ as $x\to-\infty$ and $f\to\infty$ as $x\to\infty$.

Roots. One root in each of $(-\infty,-1)$, $(-1,1)$, $(1,\infty)$: 3 real roots.

(D)