Question

Let f(x) = x³+6x²+6x and let c be the number that satisfies the Mean Value Theorem for f on the interval [-6,0].Find the Mean Value Theorem.

Answer 1

Answer:

c = 0 or c = -4

Step-by-step explanation:

According to the Mean Value Theorem

$f^{'}(c) = \frac{f(0) - f(-6)}{0 - (-6)} = \frac{0 - (-6)^3 - 6*(-6)^2 - 6*(-6)}{6} = 36 - 36 + 6 = 6$

By taking the first derivative of f

$f^{'}(x) = 3x^2 + 12x + 6$

Since$f^{'}(c) = 6$

We can solve for c

$3c^2 + 12c + 6 = 6$

$3c^2 + 12c = 0$

$c(c + 4) = 0$

c = 0 or c = -4