Answer:
0 is an inflection point
1/4 is a local maximum.
Step-by-step explanation:
To begin with you find the first derivative of the function and get that
[tex]h'(x) = 3x^2 - 12x^3[/tex]
to find the critical points you equal the first derivative to 0 and get that
[tex]3x^2 - 12x^3 = 0, x = 0,1/4[/tex]
To find if they are maximums or local minimums you use the second derivative.
[tex]h''(x) = 6x-36x^2[/tex]
since [tex]h''(0) = 0[/tex] is neither an inflection point, and since [tex]h''(1/4) = -3/4 <0[/tex] then 1/4 is a maximum.
