Approximate the critical numbers of the function shown in the graph.

Question

Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.)

Approximate the critical numbers.

x=?

List the critical numbers at which each phenomenon occurs. (If an answer does not exist, enter DNE.)

relative maxima x=?

relative minima x=?

absolute maxima x=?

absolute minima x=?

Answer 1

the critical number is the origin (0,0) which is an inflection point

there are no relative maximums or minimums, and no global, absolute maximums or minimums

You might say 1 is the absolute max and -1 is the absolute minimum, but the function never reaches those points, it only approaches it as a limit, as x approaches -1 and + 1.

x =-y^3

has points (1, -1), (-1, 1) and (0,0)

or y^3 = -x

y = cube root of (-x)

y = f(x) = (-x)^(1/3) with domain restricted to -1<x< 1

and range restricted to -1<y<1