Question

If ƒ(x) = x^2/3 then –

• A. (0, 0) is a point of maximum
• B. (0, 0) is not a point of minimum
• C. (0, 0) is a critical point
• D. ) There is no critical point

Answer 1

Answer: (C)

(0, 0) is a critical point

Answer 2

= $\frac { 2 } { 3 }$x^–1/3. This derivative is never zero, but there is no derivative for x = 0. So (0, 0) is a critical point. If x < 0 then < 0 and if x > 0 then $\frac { d y } { d x }$ > 0. Thus (0, 0) is a point of minimum.