For f(x) = x8 /9 −x17 /9 find the critical numbers.?

Question

For f(x) = x8 /9 −x17 /9 find the critical numbers.?

and also: which one is true, which one false?

a) If c is not a critical point of f, then c is not a local minimum of f.
b) If f does not have an absolute maximum on [a,b] then f is not continuous on [a,b].
c) If f has a local maximum or minimum at c, then c is a critical number of f.
d) If f has an absolute maximumon [a,b], then f must be continuous on [a,b].
e) If f has an absolute minimum value at c, then f ′(c)=0.
f) The function f(x)=x3 has a critical point on the interval [−2,2] but g) it does not have a local maximum or local minimum on that interval.

Answer 1

a) T
b)T
c)T
d)F
e)F
f)T
f´(x) = 1/9(8x^7-17x^16) = 1/9x^7(8-17x^9) x= 0 and x= (8/17)^1/9=
0.91966. The other roots are complex ones