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Attempt following question by selecting a choice to answer. B
Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = ln x on [1, e].f BA. B1e1B. B0 C. B1 D. B1  eE. Be  1
B
E
Step 1: f(x) = ln x[Write the function.]
Step 2: Since f(x) is continuous in [1, e] and differentiable in (1, e), Mean Value Theorem is applicable.
Step 3: f(1) = ln 1 = 0[Find f(1).]
Step 4: f(e) = ln e = 1[Find f(e).]
Step 5: f ′(x) = 1x[Find f ′(x).]
Step 6: f ′(c) = 1c[Find f ′(c).]
Step 7: By Mean Value Theorem, there exists c ∈ (1, e) such that f ′(c) = f(e)f(1)e1.
Step 8: 1c = 10e1
Step 9: c = e  1 ∈ (1, e)[Solve for c.]
Step 10: At c = e  1 in (1, e), the function f(x) satisfies the Mean Value Theorem.

