How do you find the maximum value of #f(x) = sinx+cosx#?
Please see the 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:
The value is a negative, therefore, we have found a maximum.