Posted by **jane** on Friday, February 27, 2009 at 1:22am.

f(x) = cos(x) - (cos(x))^2 for -pi is less than or equal to x is less than or equal to pi

1) x-intercepts?

2) x and y coordinates of all relative maximum points?

3) intervals on which f is increasing?

then i have to sketch f, so tips on doing so would be appreciated. thank you!

- calculus -
**drwls**, Friday, February 27, 2009 at 1:34am
I assume you know how to plot a graph. Choose 10 or more x values between -pi and pi, compute f(x) for each, and graph them with f(x) on the y axis. Draw a smooth line between the points.

The x intercepts are where y = 0. That would be whenever cos x = 0 or 1. You should know where those angles are x = 0 and x = pi/2 are two of them.

Compute the derivative f'(x) and set it equal to zero. The solutions of that equation will be where the function has a relative maximum or minimum.

f'(x) = -sin x + 2 sin x cos x

= sin x (2 cos x -1)

which equals 0 at x = 0, x = pi/2 and cos^1(1/2). Only the last of those is a maximum.

f is increasing where f'(x) is positive. Drawing the graph should help you find that region.

## Answer this Question

## Related Questions

- alg - the viewing window is defined by -3 is less than or equal to x is less ...
- Parametric equations/Trigonometry - Lattice points - A lattice point is a point ...
- Precalculus - A lattice point is a point with integer coordinates. How many ...
- Precalculus - A lattice point is a point with integer coordinates. How many ...
- calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...
- Math - Solving Trig Equations - Solve each equation for o is less than and/or ...
- Math - Solving for Trig Equations - Solve the following equation for 0 less than...
- Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...
- Pre-Calculus - Find the rectangular equation of the curve whose parametric ...
- Calculus - Solve & plot a graph for the following: F(X)=cos(X)-cos to second ...

More Related Questions