Chapter 4.8, Problem 3QCE

Let $f\left(x\right)=x^2-x$ .

(a) Find a point $b$ such that the slope of the secant line through $\left(0,0\right)$ and $\left(b,f\left(b\right)\right)$ is $1$ .

(b) Find all values of $c$ that satisfy the conclusion of the Mean-Value Theorem for the function $f$ on the interval $\left[0,b\right],$ where $b$ is the point found in part (a).