Applications of Derivatives
Mean Value Theorem
MMTS_Full_Test_07
Grade 12
Question:
Let $f(x)=e^x$ and $g(x)=e^{-x}$. Then, by LMVT, for $[0,1]$:
$c=(1/2)\ln(e-1)$
$c=\ln(e-1)$
$c=\ln\sqrt{e-1}$
$c=\ln(e+1)$
Step-by-Step Solution
Key Concept: LMVT: $f'(c)=(f(1)-f(0))/(1-0)$
$c=\ln(e-1)$.
Correct Answer: 3