The graph of the function f(x)=(x-4)(x+1) is shown below. which statement about the function is true?

(1) the function is increasing for all real values of X where X < 0

(2) the function is increasing for all real numbers of x where X < -1 and x>4

(3) the function is decreasing for all real numbers of x where x< 1.5

(3) the function is decreasing for all real numbers of x where x< 1.5

Step-by-step explanation:

The function given in this problem is

which can be rewritten as:

A function is:

- Increasing over a certain interval if the first derivative is positive in that interval

- Decreasing over a certain interval is the first derivative is negative in that interval

So we start by calculating the first derivative of this function. We get:

This function is positive when:

Which means, when x > 1.5.

So the function is:

- Increasing for x > 1.5

- Decreasing for x < 1.5

So the correct option is

(3) the function is decreasing for all real numbers of x where x< 1.5

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

mxb67

step-by-step explanation: