Determine the critical points of f intervals where f is

Question

Use the definition of the derivative to find f'(x) if f(x) = 3x² - 12x + 8 For f(x) = 12+ 2x² -x⁴. Determine the, following.

a. Critical points of f.

b. Intervals where f is increasing/decreasing.

c. Local maximum and minimum values of f

d. Intervals where y = f(x) is concave upward and concave downward.

e. Inflection point(s).

f Sketch the graph of y = f(x).