Question #1865

Find a number c that satisfies the Mean Value Theorem for the function
F(x) = x ^3 -2x on the interval [1,2]
Round your answers to 4 decimal places

Expert's answer

According to the Mean Value Theorem,

f'(c) = (f(b) - f(a))/(b-a) = (f(2) - f(1))/(2-1) = 4 +1 = 5

f'(c) = 3c^{2} - 2 = 5

3c^{2} = 7

c = √(7/3) = +1.5275

f'(c) = (f(b) - f(a))/(b-a) = (f(2) - f(1))/(2-1) = 4 +1 = 5

f'(c) = 3c

3c

c = √(7/3) = +1.5275

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