This means the only local extrema is {eq}x=-2 {/eq} and since the function goes from decreasing to increasing it is a local minimum. Thus we have a local minimum at {eq}x=-2 {/eq}.

The local extrema are a minimum at (2.6,-2.53) and a maximum at (1.44,2.09). Example 2 Jon wants to build a rectangular fence using 73 feet of fencing that he already owns.

Local Extrema: Local extrema can be local minima or local maxima. A local minimum is a point {eq}(x,y) {/eq} on the graph of a function that is lower than all points near it. A local maximum is a ...

If the function f(x, y) has a local extrema, then this extrema occurs at a Find a local maximum and a local minimum of the function f (X) = 1 / 3 X^2 - 2 X^2 + 3 X + 1 by taking the derivative and using the fact that a X^2 + b X + c = 0 has the solution: X = {-b plus or minu

Practice Using a Graphing Calculator to Find Local Extrema of a Polynomial Function with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost ...

The function f(x)=2x 3 −27x 2 +48x+5 as one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at x = with output value= and a local maximum at x = with output value=

- **Statement 8:** A local extremum is a \( y \)-value. #### Analyzing the Statements - Local extrema can indeed occur at the endpoints of a closed interval (Statement 2 is true, while Statement 1 is false). - Local extrema are generally considered over an open interval in the context of their definition (Statement 3 is true).

Use a graph of the function to estimate these local extrema. Find the local minimum and maximum.\\ f(x) = 2x^3-96x+42; Let f(x)= 4\sqrt{4} - x^3\ for\ x greater than or equal to 0. Find the coordinates of all local extrema and determine whether each is a local minimum or maximum. (There should be two.)

Practice Finding Local Extrema by Checking Critical Points of a Function with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your ...

For the function below, find the local extrema by using the First Derivative Test. p(x) = x^3 - 27/2 x^2 + 42x + 1. Use the First Derivative Test to find the exact location of all the relative extrema of the given function. f(t) = t^3-3t^2