Question

Suppose that f(x)=x−7x^[1/7]

(A) Find all critical values of f.
(B) Use interval notation to indicate where f(x) is increasing and also decreasing.
(C) Find the x-coordinates of all local maxima and local minima of f.
(D) Use interval notation to indicate where f(x) is concave up and also concave down.
(E) Find all inflection points of f.

Answer 1

f' = 1 - 1/x^(6/7)
so, critical values are where x=0 or x^(6/7) = 1

f is increasing where f' > 0

max/min are at critical values

concave up where f" > 0

inflection points where f" = 0