Question

At what value(s) of x does f(x) = –x^4+2x^2 have a critical point where the graph changes from decreasing to increasing?

Answer 1

f''(-1) and f''(1) are both negative, so at x=-1 and x=1, the function is changing from increasing to decreasing.

Step-by-step explanation: We usually indicate exponents with the "^" symbol. This makes the function f(x) = -x^4 + 2x^2.

f'(x) = -4x^3 + 4x; f'(x) = 0 when x= 0 or ±1.

f''(x) = -12x^2 + 4, and this is > 0 when x=0, so x=0 is a relative minimum point on the graph. This means that the function is changing from decreasing to increasing.