What if we told you that given the equation of the function, you can find all of its maximum and minimum points? Well, it's true! This process is called the first derivative test. Let's unpack it in a way that …

Are there any real functions for which the second derivative is defined but the first is not? Not necessarily across the whole function but maybe just at a single point?

Would a suitable solution be saying that at a relative maxima, the second derivative is negative, while at a relative minima, the second derivative is positive?

Practice using the second derivative test for extremum points.

Together, we apply the power rule to find the first derivative, then repeat the process to reveal the second derivative. This journey illuminates how we can use mathematical tools to uncover deeper …

The first derivative tells us where a function increases or decreases or has a maximum or minimum value; the second derivative tells us where a function is concave up or down and where it has …

Let's consider, for example, the function f (x) = x 3 + 2 x 2 . Its first derivative is f ′ (x) = 3 x 2 + 4 x . To find its second derivative, f ″ , we need to differentiate f ′ . When we do this, we find that f ″ (x) = 6 x + …

Learn how the second derivative of a function is used in order to find the function's inflection points. Learn which common mistakes to avoid in the process. We can find the inflection points of a function …

Learn how to test whether a function with two inputs has a local maximum or minimum.

For example, the first derivative tells us where a function increases or decreases and where it has maximum or minimum points; the second derivative tells us where a function is concave up or down …