Must show all work no calculator. Also answer number 16. For a particular object, a(t)= 5t^2 +6 and v(0)=3 find v(t)

For the following function, find (a) the critical numbers, (b) the open intervals where the function is increasing, and (c) the open intervals where the function is decreasing f(x) = (x - 7)e 5x a. Find the critical numbers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The critical number(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. There are no critical numbers for this function. b. Find the open intervals where the function is increasing Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is never increasing O B. The function is increasing on the open interval(s) (Type your answer in interval notation. Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed.) c. Find the open intervals where the function is decreasing Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The function is decreasing on the open interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed ) O B. The function is never decreasing