Is there an example of a function with a critical point but no local minimum or maximum?

Question

Also, why would given example be sufficient?

Answer 1

Hello Naeema,

One example is y = x³ at x = 0. The graph goes up from left to right and has no maximum or minimum anywhere if you graph it for x going from -– ∞ to ∞. The slope formula is y' = 3x² so the slope at x = 0 is 0 which makes x = 0 a critical value.