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Attempt following question by selecting a choice to answer. f
Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x^{2}  4x on [2, 4].eee fffA. f53B. f212C. f0 D. f3 E. f213 ff
D
Step 1: f(x) = x^{2}  4x[Write the function.]
Step 2: Since f(x) is continuous in [2, 4] and differentiable in (2, 4), Mean Value Theorem is applicable.
Step 3: f(2) = (2)^{2}  4(2) =  4[Find f(2).]
Step 4: f(4) = (4)^{2}  4(4) = 0[Find f(4).]
Step 5: f ′(x) = 2x  4[Find f ′(x).]
Step 6: f ′(c) = 2c  4[Find f ′(c).]
Step 7: By Mean Value Theorem, there exists c ∈ (2, 4) such that f ′(c) = f(4)f(2)42.
Step 8: 2c  4 = 0(4)2
Step 9: 2c  4 = 2
Step 10: c = 3 ∈ (2, 4)[Solve for c.]
Step 11: At c = 3 in (2, 4), the function f(x) satisfies the Mean Value Theorem.

