I really need help with my homework. Thank you!

Question

The graph below shows the graph of f (x), its derivative f ′(x), and its second derivative f ″(x). Which of the following is the correct statement?

 

Options:

1)	A is f ′, B is f, C is f ″.
2)	A is f ″, B is f, C is f ′.
3)	A is f ′, B is f ″, C is f.
4)	A is f, B is f ′, C is f ″.

Answer 1

B is f(x)

A is f'(x)

C is f''x)

Answer 2

The best way to tackle a problem like this is to draw out the derivative of each line by drawing tangents from the lines representing the slopes and then plotting these slopes. If you do this, you will see that line A has a positive slope that decreases to 0 (which happens to also be at the origin), before becoming positive again. This is similar to the plot of Line B as it starts at a positive y value, decreases to zero, and then increases to positive y values again.

Line B has a negative slope that decreases to zero, and then becomes positive. This is similar to the plot of Line C which starts at negative values that decrease to 0, and then increase to positive values.

Line C has a constantly positive slope. None of the other lines have constant positive y values.

Therefore the correct answer is D: A is f, B is f ' C is f ''

Something to keep in mind as you check your work. The derivative of a cubic function is a quadratic, and the derivative of a quadratic is a line. If f(x) = x³, then f '(x) = 3x², and f ''(x) = 6x. If you look at the three functions graphed, line A seems to be cubic, line B seems to be quadratic, and line C seems to be linear.

Therefore the correct answer is D: A is f, B is f ' C is f ''