5. The figure shows the graphs of $f, f^{\prime}$, and $f^{\prime \prime}$. Identify each curve, and explain your choices.

Step-by-Step Solution

To determine

To identify:

f,f'&f''

Answer

a) Curve a is f

b) Curve c is f'

c) Curve b is f''

Explanation

Curve a is increasing for x<0 and decreasing for x>0 thus curve of its derivative must be first increasing and then decreasing and this condition is satisfy by curve c

Curve c is first increasing then decreasing and again increasing so curve of its derivative is increasing first then decreasing and again increasing and this condition is only satisfied by curve b hence it is curve of second derivative of f

Conclusion:

Hence by observing graph we conclude that curve a is f, curve c is f' and curve b is f''