Question

HELP ASAP!!! 40 POINTS
Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x2 + 5x − 12 belongs to the interval (-1, 1).

Answer 1

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

What is the slope of the tangent line to a function f(x) at point x = x0?

It is given by the derivative at x = x0, that is:

$m = f^{\prime}(x_0)$.

In this problem, the function is:

$f(x) = 0.2x^2 + 5x - 12$

Hence the derivative is:

$f^{\prime}(x) = 0.4x + 5$

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

More can be learned about derivatives and tangent lines at https://brainly.com/question/8174665

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