Calculus I: Find the smaller and larger x value.​

Answers:

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Explanation:

Apply the derivative (see attached image for the steps)

You should get

The line y = x is really y = 1x+0. We see that it's in the form y = mx+b with m = 1 as the slope. The negative reciprocal of this is m = -1, which is the perpendicular slope. As a rule, any two perpendicular lines always have their slopes multiply to -1 as long as neither line is vertical or horizontal.

So we want the derivative we just found to be set equal to -1, that way we have the x value lead to this derivative slope value.

We want dy/dx = -1

In short, the equation we need to solve is

Let's solve for x

The smaller x value is -3 while the larger x value is x = -1.