a. find the open interval(s) on which the function is increasing and decreasing.\nb. identify the functions…

a. find the open interval(s) on which the function is increasing and decreasing.\nb. identify the functions local and absolute extreme values, if any, saying where they occur.\ng(t) = -2t² + 3t - 1\na. find the open intervals on which the function is increasing. select the correct choice below and fill in any answer boxes within your choice.\na. the function is increasing on the open interval(s) \n(type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\nb. the function is never increasing.

a. find the open interval(s) on which the function is increasing and decreasing.\nb. identify the functions local and absolute extreme values, if any, saying where they occur.\ng(t) = -2t² + 3t - 1\na. find the open intervals on which the function is increasing. select the correct choice below and fill in any answer boxes within your choice.\na. the function is increasing on the open interval(s) \n(type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\nb. the function is never increasing.

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of (g(t)=- 2t^{2}+3t - 1) is (g^{\prime}(t)=-4t + 3).

Step2: Find the critical point

Set (g^{\prime}(t) = 0), then (-4t+3 = 0). Solving for (t) gives (t=\frac{3}{4}).

Step3: Determine the intervals of increase and decrease

Choose a test point in the interval ((-\infty,\frac{3}{4})), say (t = 0). Then (g^{\prime}(0)=-4\times0 + 3=3>0). Choose a test point in the interval ((\frac{3}{4},\infty)), say (t = 1). Then (g^{\prime}(1)=-4\times1+3=-1<0).

Answer:

A. The function is increasing on the open interval((-\infty,\frac{3}{4}))