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Attempt following question by selecting a choice to answer. D
Find the value in the interval, which satisfies the Mean Value Theorem for the function f(x) = x43 on [ 1, 1].BBBB DDDDA. D43B. D0 C. D1 D. D34E. D 1 DD
B
Step 1: f(x) = x43[Write the function.]
Step 2: Since f(x) is continuous in [ 1, 1] and differentiable in ( 1, 1), Mean Value Theorem is applicable.
Step 3: f( 1) = (1)43 = 1[Find f( 1).]
Step 4: f(1) = (1)43 = 1[Find f(1).]
Step 5: f ′(x) = 43x13[Find f ′(x).]
Step 6: f ′(c) = 43c13[Find f ′(c).]
Step 7: By Mean Value Theorem, there exists c ∈ ( 1, 1) such that f ′(c) = f(1)f(1)1(1).
Step 8: 43c13 = 0
Step 9: c = 0 ∈ ( 1, 1)[Solve for c.]
Step 10: At c = 0 in ( 1, 1), the function f(x) satisfies the Mean Value Theorem.

