Let g(x)=x^3+12x^2+36xg(x)=x 3 +12x 2 +36xg, left parenthesis, x, right parenthesis, equals, x, start superscript, 3, end superscript, plus, 12, x, start superscript, 2, end superscript, plus, 36, x and let ccc be the number that satisfies the mean value theorem for ggg on the interval -8\leq x\leq-2−8≤x≤−2minus, 8, is less than or equal to, x, is less than or equal to, minus, 2.

Answer with Step-by-step explanation:

Mean value theorem:If a function f(x) is continuous on [a,b] and differentiable on (a,b).Then there exist a number such that

We are given that a=-8 and b=-2

substitute x=c then we get

Substitute the values in the formula

Quadratic formula for

Using the quadratic formula

and

and

c=-1.789 does not lie in the interval [-8,-2]

But c=-6.21 lies in the interval

Hence, the function satisfied the mean value theorem.

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step-by-step explanation: