consider the function on the intervals (0,2pi)

Question

Consider the function on the interval (0, 2π).

f(x) = 8 sin2(x) + 8 sin(x)

(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)

Answer 1

f(x) = 8 sin2(x) + 8 sin(x)

(a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.)

increasing _(0,π/2) (3.665, 4.71) (5.76, 6.28)_____

decreasing _π/2, 3.665) (4.71, 5.76)_____

(b) Apply the First Derivative Test to identify all relative extrema.

f'(x) = 16SinxCosx + 8Cosx = 8Sin2x + 8Cosx

relative maxima (x, y) = (_5.76___) (smaller x-value)

(x, y) = (_4.71___) (larger x-value)

relative minima (x, y) = (_3/665___) (smaller x-value)

(x, y) = (_4.71___) (larger x-value)