Find all inflection points for the function f(x)=x4-24x2+11

Question

Find all inflection points for the function f(x)=x⁴-24x²+11

a) {2} ;

b) {−2};

c) {−2; 2};

d) doesn’t exist.

Answer 1

First, find the derivative:

f' (x) = 4x³ - 48x this tells us there will be 3 roots: x=0, and x = +/- √(12)

Second derivative:

f" (x) = 12x² -48

x = +/- 2

So---inflection points at x = 2 and x = -2 (impossible to see on a graph without stretching the x-axis)

Answer 2

The 2nd derivative is 12x² - 48.

The points of inflection should occur at x = 2 and x = -2 and a graph will confirm that this is correct.