Question

(b) Locate the critical points and determine their nature for the function

f(x)=-2x2+1/4x2

Answer 1

$$f(x) = -2x^2 + \frac{1}{4x^2};$$ $$f'(x) = -4x - \frac{1}{2x^3};$$

To locate the critical points:

$$f'(x) = 0;$$ $$\frac{8x^4 + 1}{2x^3} \simeq 0;$$ $$x^4 = -\frac{1}{8}, \text{ no solutions}$$ $$x \neq 0, \text{ so } x = 0 \text{ — critical point}$$

Type of critical point is that where $f'(x)$ is undefined.