#### To determine

**To identify:** The curves f,f′ and f′′ on given graph with proper explanation.

#### Answer

In the given graph,a=f, b=f′ and c=f″.

#### Explanation

**Graph:**

The given graph is shown as in Figure 1,

**Observation:**

From the Figure 1, it is observed that the point where c(x)=0 is the same point where graph of b(x) has horizontal tangent.

Recall that the derivative of a function is zero where the function has a horizontal tangent.

Therefore, c(x) is the derivative of the graph b(x). That is, b′(x)=c(x).

Observe the graph of *a* and *b* carefully.

The point where b(x)=0 is the same point where graph of a(x) has horizontal tangent.

Recall that the derivative of a function is zero where the function has a horizontal tangent.

Therefore, b(x) is the derivative of the graph a(x). That is, a′(x)=b(x).

From Figure 1, it is observed that, neither a(x) nor b(x) are equal to zero where the graph of c(x) has horizontal tangent. Clearly, f″=c(x).

Use the above information a′(x)=b(x) and b′(x)=c(x) to concluded that a″(x)=c(x).

Thus, a=f,b=f′, and c=f″.