The function f(x)=e^x satisfies the Mean Value Theorem on [0,1]. The value of cin(0,1) guaranteed by MVT satisfies:

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SSC Pure Mathematics QUESTION #1283

Question 1

The function \(f(x)=e^x\) satisfies the Mean Value Theorem on \([0,1]\). The value of \(c\in(0,1)\) guaranteed by MVT satisfies:

Correct Answer Explanation

By MVT: \(f'(c)=\dfrac{f(1)-f(0)}{1-0}=\dfrac{e-1}{1}=e-1\). Since \(f'(x)=e^x\), we get \(e^c=e-1\). Since \(1