Question

Which of the following function satisfies hypotheses and the conclusion of the Lagrange Mean Value Theorem

• A. $f(x) = |x|$ on $[-1, 1]$
• B. $f(x) = \sqrt{x}$ on $[-1, 1]$
• C. $f(x) = \sqrt[3]{x}$ on $[-1, 1]$
• D. $f(x) = 2x^2 - 7x + 10$ on $[2, 5]$

Hint:

Polynomials, exponential functions, $\sin(x)$, and $\cos(x)$ are everywhere continuous and differentiable. They always satisfy LMVT on any finite interval $[a,b]$. Watch out for $|x|$, $x^{1/3}$, or fractions with zero in denominators inside $(a,b)$.

Answer 1

The Correct Option is D