The function given below satisfies the Mean Value Theorem on the specified interval. Find the value of c in the interval (1,2) where
f′(c) = f(b)−f(a)/
b−a

f(x)=x^3−1.7x;[1,2]

Question

The function given below satisfies the Mean Value Theorem on the specified interval.  Find the value of c in the interval (1,2) where
f′(c) = f(b)−f(a)/
        b−a

f(x)=x^3−1.7x;[1,2]

az_lender · Accepted Answer

The derivative is 3x^2 - 1.7.
We have f(2) = 8 - 3.4 = 4.6, and f(1) = -0.7.
So the [f(b) - f(a)]/(b-a) would be 5.3/1 = 5.3.

So we are looking for a point "c" where f'(c) = 5.3, that is to say,
3c^2 - 1.7 = 5.3 => 3c^2 = 7 => c = sqrt(7/3) = around 1.52 but use a calculator.

The function given below satisfies the Mean Value Theorem on the specified interval. Find the value of c in the interval (1,2) ?

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