Answer:
Juan runs 7/10 of a mile every hour
Step-by-step explanation:
First find out how much he ran every 1/7 of an hour
2/5 x 1/4 = 4/7 x 1/4
1/10 = 1/7
1/10 x 7 = 1/7 x 7
7/10 = 1
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.