Is f(x)=cos(-x) increasing or decreasing at x=0?

1 Answer
Apr 6, 2018

f(x)=cos(-x) is neither increasing nor decreasing at x=0

Explanation:

The first derivative provides the slope at each point of our function. A positive slope means the function is increasing and that a negative slope means that the function is decreasing.

Knowing this, we can find out if cos(-x) is increasing or decreasing at color(red)(x=0) by evaluating its first derivative at that point.

Before starting, we may want to simplify our function. Because cos(x) is an even function, we know that cos(-x)=cos(x).

d/dx[cos(x)]

= -sin(x)

Evaluate at color(red)(x=0):

-sin(color(red)0)

= -0

= 0

In this case, the slope is neither negative or positive, but 0. Hence, f(x)=cos(-x) is neither increasing nor decreasing at color(red)(x=0).