Question

Approximate the relative and absolute extrema of the function f(x). Please explain how you got the answer too, please!!

a) Relative Extrema at critical points
b) Absolute Extrema at endpoints
c) No extrema exist
d) Extrema cannot be determined

Answer 1

To approximate the relative and absolute extrema of a function, follow these steps: (a) Find the critical points, evaluate the function to determine if they are relative extrema. (b) Evaluate the function at the endpoints to find the absolute extrema. (c) If no critical points exist and the function is continuous, no extrema exist; if the function is not continuous or there are vertical asymptotes, the extrema cannot be determined.

Step-by-step explanation:

To approximate the relative and absolute extrema of a function, you need to follow certain steps:

a) To find the relative extrema, you need to identify the critical points of the function. These are the points where the derivative of the function equals zero or is undefined. Then, you can evaluate the function at these points to determine if they correspond to relative maximum or minimum points.

b) To find the absolute extrema, you need to evaluate the function at the endpoints of the interval. The highest value will correspond to the absolute maximum, and the lowest value will correspond to the absolute minimum.

c) If there are no critical points and the function is continuous over the interval, then no extrema exist. On the other hand, if the function is not continuous or there are vertical asymptotes, the extrema cannot be determined.

Answer 2

To approximate the relative and absolute extrema of a function, follow these steps: (a) Find the critical points, evaluate the function to determine if they are relative extrema. (b) Evaluate the function at the endpoints to find the absolute extrema. (c) If no critical points exist and the function is continuous, no extrema exist; if the function is not continuous or there are vertical asymptotes, the extrema cannot be determined.

Step-by-step explanation:

To approximate the relative and absolute extrema of a function, you need to follow certain steps:

a) To find the relative extrema, you need to identify the critical points of the function. These are the points where the derivative of the function equals zero or is undefined. Then, you can evaluate the function at these points to determine if they correspond to relative maximum or minimum points.

b) To find the absolute extrema, you need to evaluate the function at the endpoints of the interval. The highest value will correspond to the absolute maximum, and the lowest value will correspond to the absolute minimum.

c) If there are no critical points and the function is continuous over the interval, then no extrema exist. On the other hand, if the function is not continuous or there are vertical asymptotes, the extrema cannot be determined.