Question

For the function below, find (a) the critical numbers, (b) the open intervals where the function is increasing, and (c) the open intervals where it is decreasing f(x)=2.3+16x-0.3x² CTT

Answer 1

critical number: 26.6667

increasing from (-∞, 26.6667) and decreasing from (26.6667,∞)

Explanation:

1) find the derivative:

derivative of f(x) = 16-0.6x

2) Set derivative equal to zero

16-0.6x = 0

0.6x = 16

x = 26.6667

3) Create a table of intervals

(-∞, 26.6667) | (26.6667, ∞)

1 27

Plug in these numbers into the derivative

+ -

So It is increasing from (-∞, 26.6667) and decreasing from (26.6667,∞)