Question

The function f(x) = - 2x ^ 3 + 3.66x ^ 2 + 78.5808x - 7.46 is increasing on the open interval (

Answer 1

Given the function:

$f(x)=-2x^3+3.66x^2+78.5808x-7.46$

• You can graph it using a graphing tool:

You can identify the intervals on which the function is increasing and the intervals on which it is decreasing:

Notice that it increases on this interval:

$(-3.06,4.28)$

Notice that it decreases on these intervals:

$(-\infty,-3.06)\text{ }and\text{ }(4.28,\infty)$

• By analyzing the graph. you can identify this Local Maximum (the highest y-value on the interval):

$y=239.106$

Hence, the answers are:

• The function is increasing on the open interval:

$(-3.06,4.28)$

• It is on the open intervals:

$(-\infty,-3.06)\text{ }and\text{ }(4.28,\infty)$

• The function has a local maximum at:

$y=239.106$