Question

How can you tell if the slope of a tangent line belongs to a certain interval?

The question is: 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).
Im confused cause I dont know how to tell wheather or not the slope belongs to that interval or not

Answer 1

-14, -12, -10.5

Explanation:

Just answered the question

Answer 2

The slope of the function is given by its derivative. You want to find the values of x such that the derivative is between -1 and 1.

... f'(x) = 0.4x +5

... -1 < 0.4x +5 < 1 . . . . . your requirement for slope

... -6 < 0.4x < -4 . . . . . . subtract 5

... -15 < x < -10 . . . . . . . multiply by 2.5

Any value of x that is between -15 and -10 will be one where the tangent line has a slope between -1 and 1.

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The graph shows tangent lines with slopes of -1 and +1. You can see that the slope of the graph of f(x) is between those values when x is between the tangent points.