Question

The function f(x) = - 2x ^ 3 + 36x ^ 2 - 192x + 10 has one local minimum and one local maximum .

Answer 1

Given:

`f(x)=-2x^3+36x^2-192x+10`

To determine the local maximum and the local minimum of the given equation, we check the graph first as shown below:

We also note that local maximum and minimum points on a function's graph stand out rather noticeably, making them helpful for interpreting the graph's overall shape. The points of the functions that define the maximum and minimum range are local maximum and minimum.

As we can see, the point that has the minimum range is at point (4,-310), while the point that has the maximum range is at point (8,-246).

Therefore, this function has a local minimum point at x=4 with value equal to -310 and a local maximum at x=8 with value equal to -246.