# How do you find the maximum value of #f(x) = sinx+cosx#?

##### 1 Answer

Please see the explanation.

#### Explanation:

The x coordinates of extrema can be found by, computing the first derivative, setting that equal to zero, and then solving for x:

Compute the first derivative:

Set equal to zero:

Solve for x:

Because the tangent function has a period of

To determine whether this is a maximum, perform the second derivative test, using one of the values:

Evaluate at

The value is a negative, therefore, we have found a maximum.