A number $a$ is called a fixed point of a function $f$ if $f(a)=a$. Consider the function $f(x)={x}^{87}+4x+2$, $x\in \mathbb{R}$.

(a) Use the Mean Value Theorem to show that $f(x)$ cannot have more than one fixed point.

(b) Use the Intermediate Value Theorem and the result in (a) to show that $f(x)$ has exactly one fixed point.

(a) Use the Mean Value Theorem to show that $f(x)$ cannot have more than one fixed point.

(b) Use the Intermediate Value Theorem and the result in (a) to show that $f(x)$ has exactly one fixed point.