Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 8 (a) find the open interval(s) on which the function is increasing or decreasing. (enter your answers using interval notation.) increasing decreasing (b) apply the first derivative test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (x, y) = (larger x-value) relative minima (x, y) = (smaller x-value) (x, y) = (larger x-value)

a) Increasing in

decreasing

Local maximum

Local minimum

Step-by-step explanation:

Let f(x) be

f(x) = sin(x)+cos(x)+0 for 0<x<2π.

Taking the first derivative

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

The critical points are those where the derivative vanishes.

f'(x) = 0 iif cos(x) = sin (x), so, the critical points in (0, 2π) are

To find out what kind of critical points they are, we take the second derivative

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

Evaluate this expression at the critical points

so, this point is a local maximum.

and here we have a local minimum.

The function then is increasing in the intervals

and decreasing in

good job you smart son of a gun you are smarter that einstein. 7

if i put something wrong your not gonna like it so rather not say nothing.