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

The second derivative at x = 0 is: f ″ (x) = 12 x 10 = 12 (0) 10 = 10 We choose 1 to test the concavity of the graph on the right of the possible inflection point x = 5 6.

Math Calculus Calculus questions and answers This problem illustrates the Second Derivative Test.

Show that the Second Derivative Test is inconclusive when applied to the following function at (0,0). Describe the behavior of the function at the critical point. f (x,y)=sin (x?y2) First, …

Question: 8. For the following functions find all of the critical points and then classify them using the second derivative test. (a) f (L, y) = x3 – 2xy + 8y3. (b) g (x,y) = 3x2 + y3 - 6ry. (c) h (x,y) = …

For what values of the constant k does the Second Derivative Test guarantee that f (x,y) = x² + kxy + y2 will have a saddle point at (0,0)? A local minimum at (0,0)?

Discover what a second derivative is and how second derivatives can be used to learn more about functions. Observe examples of implicit and explicit second-degree differentiation for …

Question: Find the local maximum and minimum values of the function f (x)=−x−x64 using the Second Derivative Test. Complete the table below. Enter the points in increasing order of their …

Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. If the Second Derivative Test is …

Find the critical points of the given function. Then use the second derivative test to determine if the critical points correspond to local maxima, local minima, or saddle points of the graph of …