whats the difference between the first and the second derivative tests?

Question

in the explanation below, what is the time being drawn... i dont getit...

Answer 1

The main difference is that the first derivative test requires use of only the first derivative, while the second derivative test requires use of the first and second derivatives. Therefore, the first derivative test can be used in situations where the function is not twice differentiable, while the second derivative test cannot. Also, the first derivative test involves an examination of the value of the first derivative in the neighborhood of a value of interest while the second derivative test only requires that you examine the values of the first and second derivative at the individual point.

Answer 2

the first derivative test needs to draw a time for sign of the first derivative

But, second derivate test does not need a time to draw.
Only by comparing you can give your decision max or min.