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

Mathematics

2 answers:

Vaselesa [24]3 years ago

6 0

Answer:

-14, -12, -10.5

Step-by-step explanation:

Just answered the question

Mila [183]3 years ago

5 0

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.

_____

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.

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