6) Find any relative extrema of y- arcsinx-x 1-X 7. The base of a 20 foot tall e

Question

6) Find any relative extrema of y- arcsinx-x 1-X 7. The base of a 20 foot tall exit sign is 30 feet above the driver's eye level. When cars are far away, the sign is hard to read because of the distance. When they are close, the sign is hard to read because the driver has to look up at a steep angle. The sign is easiest to read when the distance x is such that the angle at the driver's eye is as large as possible. a) Write as the difference of 2 inverse tangents. Exit 20 ft 1Mile ahead b) write an equation for dr 30 ft Car c) The sign is easiest to read at the value ofx where stops increasing and starts decreasing. This happens when0. Find x and confirm using the calculator dit

Explanation / Answer

To find the relative extrema, find the derivative of the given function and set equal to zero.

y(x)=arcsin(x)-x

y'(x)=1/sqrt(x^2-1) - 1

Then, equate to zero.

1/sqrt(x^2-1)-1=0

1/sqrt(x^2-1)=1

sqrt(x^2-1)=1

x^2-1=1

x^2=1

x= plus or minus 1

These are extrema points of the given function.

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