Graph Analysis Review

when is the function f(x)=x²+6x+9 increasing?

• (3,∞)

• (-∞,3)

• (-3,-∞)

• (-3,∞)

At which point(s) will the slopes of the tangent line be zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

When does a curve have a horizontal tangent line?

• When x = 0

• When y = 0

What is the justification for a function to be decreasing?

• Function is increasing

• First Derivative is Positive

• First Derivative is Negative

• Second Derivative is Positive

Given the graph of the derivative of a function, how can you tell if the function is concave up.

• The graph is positive

• The graph changes from positive to negative

• The graph changes from negative to positive

• The graph is increasing

What is the justification for a function having a local minimum?

• The derivative changes from positive to negative

• The derivative changes from negative to positive

• The derivative changes from increasing to decreasing

• The derivative changes from decreasing to increasing?

What can you conclude from this number line?

• there is a maximum for A at 12

• there is a minimum for A at 12

• you will have a profitable year

• the stars are aligning nicely

Pick the correct interpretation from the given number line for V', the derivative of V.

• V has a minimum at 3

• V has a maximum at both 1 and 5

• V has a maximum at 0 and a minimum at 6

• V has a maximum at 1 and a minimum at 5

The function shown is the graph of f '(x), the derivative of f(x). The domain is [-3,5]. On which interval is the graph of f(x) concave upward?

• (-1,1) & (3,5]

• [-3,-2) & (4,5]

• [-3,-1) & (1,3)

• (-2,1) & (1,4)

This graph is of the first derivative, f' (x). For what value of x does f have a relative maximum?

• x = 0

• x = 1

• x = 2

• x = 4

• x = 5