answer the following questions about the function whose derivative is $f(x)=(x - 6)^2(x + 7)$\na. what are…

answer the following questions about the function whose derivative is $f(x)=(x - 6)^2(x + 7)$\na. what are the critical points of $f$?\nb. on what open intervals is $f$ increasing or decreasing?\nc. at what points, if any, does $f$ assume local maximum and minimum values?\na. find the critical points, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n○ a. the critical point(s) of $f$ is/are $x =$\n(simplify your answer. use a comma to separate answers as needed.)\n○ b. the function $f$ has no critical points

answer the following questions about the function whose derivative is $f(x)=(x - 6)^2(x + 7)$\na. what are the critical points of $f$?\nb. on what open intervals is $f$ increasing or decreasing?\nc. at what points, if any, does $f$ assume local maximum and minimum values?\na. find the critical points, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n○ a. the critical point(s) of $f$ is/are $x =$\n(simplify your answer. use a comma to separate answers as needed.)\n○ b. the function $f$ has no critical points

Answer

Explanation:

Step1: Find critical points

Critical points occur where (f^{\prime}(x) = 0). Set ((x - 6)^{2}(x + 7)=0). Using the zero - product property: if (ab = 0), then (a = 0) or (b = 0). For ((x - 6)^{2}=0), we have (x-6 = 0), so (x = 6). For (x + 7=0), we have (x=-7).

Answer:

A. The critical point(s) of (f) is/are (x=-7,6)