Recent questions tagged mean-value-theorem

Suppose $f$ and $g$ are continuous real valued functions on $[a, b]$ and are differentiable on $(a, b)$. Assume that $g^{\prime}(x) \neq 0$ for any $x \in(a, b)$. Prove t...

Find a point on the graph of y=x3(cube) where the tangent is parallel to the chord joining (1,1) and (3,27).

If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___