Differentiate and classify the zeros of f'(x)=0.

f'(x) = 85 x^4 - 42 x^2,

so the solutions of f'(x)=0 are x=0, and +/- sqrt(42/85).

Now the second derivative f''(x) = 340 x^3 - 84 x, so the second derivative

test tells us that x=+sqrt(42/85) is a local minimum, and x=-sqrt(42/85) is a

local maximum.

f''(0)=0, so we need to classify x=0 by other means: As f(x) is an odd order

polynomial it has an equal number of maxima and minima, but here we have

three roots for f(x)=0, so f(0) must be a point of inflection.

RonL