Graphing functions

Which of the following is true about the graph of the polynomial functions?

I. The relative maximum is at ( 0,-5).

II. The relative minimum is at ( -3,-4).

III. The relative maximum is at ( -5,0).

IV. The relative minimum is at ( -4,-3).

• I and IV

• I and II

• III and IV

• II and III

Given      $f\left(x\right)=-7x^2+5$  

Use the First Derivative Test to find the open interval in which f(x) is increasing or decreasing. Select ALL that apply.

• Decreasing at   $\left(-\infty,-7\right)$  

• Increasing at $\left(-\infty,\ 0\right)$  

• Decreasing at $\left(0,\ \infty\right)$  

• Increasing at    $\left(-7,\infty\right)$  

• Decreasing at   $\left(-\infty,0\right)$  

How many extrema are there in this graph?

• 2 max, 2 min

• 3 max, 2 min

• 2 max, 3 min

• 3 increasing intervals, 2 decreasing intervals

• 2 increasing intervals, 3 decreasing intervals

In section A, the graph is

• Increasing

• Decreasing

• Constant

Which is the interval of increasing for the graph? Assume there are arrows on the graph.

• (-∞, 1)

• (1, ∞)

• (-∞, ∞)

• (1, 5)

Answer explanation

Look for where the graph is going UP. Base the interval on the x-values. If there is an arrow pointing left, it goes back to negative infinity. If there is an arrow pointing right, it goes to positive infinity.

Which statement is true about this function?

• The function is never constant
• The function is always increasing
• The function is never decreasing
• The function increases on the interval 11:00 < x < 15:00

Find local maximum and local minimum values of the function f ( x) =

 $x^3-3x$  

• -1 , 1

• 2 , -2

• 2 , -1 

• 1 , 0 

 $f\left(x\right)=\left(x+1\right)\left(x-3\right)^2$  

Which statement is NOT true about the graph of  $f\left(x\right)$  ?

• There is an inflection point at x = 3

• There is an x-intercept at x = -1

• There is a y-intercept at x = 3

• There is a relative minimum at (3, 0)

• There is a relative maximum at x  =  $\frac{1}{3}$  

When is this function increasing?

• (-3, ∞)

• (-2.5, 2.5)

• (-3, 3)

• (3, ∞)

What is the x coordinate of the local maximum?

• 1.5

• 3.9

• 8.8

• -60.6

• does not exist for this function