Question

Consider the following function: f(x) = x² - 21x - 40000. (a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.) (b) Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.) (c) Find the local minimum and maximum value of f.

Answer 1

To find intervals of increasing and decreasing, find critical points and analyze the derivative change. Use the first and second derivative tests to find local minimum and maximum values.

Step-by-step explanation:

To determine the intervals on which the function f(x) = x² - 21x - 40000 is increasing or decreasing, you need to find the critical points. The critical points occur where the derivative equals zero or does not exist. To find local minimum and maximum values, you can use the first and second derivative tests. By finding the values of x where the derivative changes sign, you can determine the intervals on which f(x) is increasing or decreasing. By analyzing the second derivative, you can identify the local minimum and maximum values of f(x).