J. M.
asked • 12/07/23FInd the values of c
find the value or values of c that satisfy the equation f(b)-f(a) / b-a=f'(c) in the conclusion of the Mean Value Theorem for the following function and interval. f(x)= 3x^3 + 4x^2, [-2, 2]
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1 Expert Answer
Yefim S. answered • 12/07/23
Tutor
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Math Tutor with Experience
f'(x) = 9x2 + 8x; f(-2) = - 24 + 16 = - 8; f(2) = 24 + 16 = 40;
f'(c) = 9c2 + 8c = (40 + 8)/(2 + 2) = 12; 9c2 + 8c - 12 = 0; c = (- 4 ±√16 + 108)/9 = (- 4 ± 2√31)/9
c1 = - 1.866, c2 = 0.793
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Doug C.
This Desmos graph gives you an opportunity to look over the solution taking some notes along the way to come to an understanding of what the Mean Value Theorem is all about. Take a look, then comment on any part you do not understand. desmos.com/calculator/zusdwjiwlx12/07/23