Master the second derivative test with our engaging video lesson. Explore real-life uses, then boost your knowledge in calculus with an optional quiz.

Learn to define what first derivatives are. Learn how to find the first derivative of functions. Discover the first derivative formula and see examples.

Note the sign of f ′ (x) since the sign of the first derivative indicates if the function is increasing or decreasing on the interval. For the interval (∞, 2), we can test the sign of the ...

Learn how to find the location of relative extrema of a function using the first derivative, and see examples that work through sample problems step-by-step to improve your math knowledge …

Learn the definition of concavity and how to find inflection points. Understand the step-by-step processes for finding inflection points and intervals of concavity.

The First Derivative Test is a test in calculus which is used to determine the relative extrema of a given function. It uses the first derivative of the function to determine the critical points, and …

The first derivative test is inconclusive if the function hasn't slope of the tangent line at this point, for example, the function has a vertical... See full answer below.

1) The graph of the following function has one relative maximum point and one relative minimum point. Find these points using the first derivative test. f (x) = x 3 6 x 2 + 9 x + 4 2) The graph of …

First Derivative Test: Suppose f (x) be a differentiable function defined on an interval I and let a ∈ I . Then, (a) x is a point of local maximum value of f (x) if f ′ (x)> 0 at every point sufficiently …

Question: Given {eq}f (x) = x^ {2} - 4x {/eq}, (a) find the critical numbers of f (if any), (b) find the open interval (s) on which the function is increasing or decreasing, (c) apply the First …