Graphs of f, f', and f''

The function f is defined on the closed interval [0,8]. The graph of its derivative, f', is shown above.

The point (3,5) is on the graph of y = f(x). An equation of the line tangent to the graph of f at (3,5) is:

• $y=2$

• $y=5$

• $y-5=2\left(x-3\right)$

• $y+5=2\left(x-3\right)$

• $y+5=2\left(x+3\right)$

The function f is defined on the closed interval [0,8]. The graph of its derivative, f', is shown above.

How many points of inflection does the graph of f have?

• 2

• 3

• 4

• 5

• 6

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The function f is defined on the closed interval [0,8]. The graph of its derivative, f', is shown above.

On what interval(s) is f decreasing?

• (6,8)

• (1,6)

• (1,2), (3,4), and (5,7)

• (0,1), (2,3), (4,5), and (7,8)

• The function is always increasing

The function f is defined on the closed interval [0,8]. The graph of its derivative, f', is shown above.

Where does the graph of f have a local maximum?

• x = 0

• x = 1

• x = 4

• x = 6

• x = 8

The function f is defined on the closed interval [0,8]. The graph of its derivative, f', is shown above.

At what value of x does the absolute minimum of f occur?

• x = 0

• x = 2

• x = 4

• x = 6

• x = 8

The second derivative of the function f is given by

 $f''\left(x\right)=x\left(x-a\right)\left(x-b\right)^2$  .  The graph of f'' is shown above.
Where is f concave down?

•  $\left(a,0\right)$  

•  $\left(-\infty,j\right)\ ,\ \left(k,b\right)$  

•  $\left(0,b\right)$  

•  $\left(0,\infty\right)$  

•  $\left(j,k\right)\ ,\ \left(b,\infty\right)$  

The second derivative of the function f is given by

 $f''\left(x\right)=x\left(x-a\right)\left(x-b\right)^2$  .  The graph of f'' is shown above.
For what values fo x does the graph fo f have a point of inflection?

• 0 and a only

• 0 and m only 

• b and j only

• 0, a, and b

• b, j, and k

The graphs of the derivatives of the functions f, g, and h are shown above. Which of the functions have a relative maximum on the open interval a < x < b?

• f only

• g only

• h only

• f and g only

• f, g, and h

The graphs of the derivatives of the functions f, g, and h are shown above. Which of the functions have a relative minimum on the open interval a < x < b?

• f only

• g only

• h only

• f and g only

• f, g, and h

The graph of f is shown in the figure above. Which of the following could be the graph of the derivative of f?

• 
• 
• 
• 

Tags

CCSS.HSF.IF.B.4