#### To determine

**To Identify:** The curves f,f′,f′′ and f‴ on given graph and give proper explanation.

#### Answer

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

#### Explanation

**Graph:**

The given graph is shown as in Figure 1,

**Observation:**

Observe the graph of *c* and *d* carefully.

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

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

c(x) is the derivative of the graph d(x).

Thus, d′(x)=c(x). (1)

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

The slope of *c* has negative value when x<0. Only the curve *b* has negative value when x<0. Also, it is observed that the slope of *c* has positive value when x>0 while the curve *b* has positive value when x>0.

Thus, c′(x)=b(x). (2)

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

The slope of *b* has positive value when x∈ℝ−{0}. Only the curve *a* has positive value when x∈ℝ.

Thus, b′(x)=a(x). (3)

From (1), (2) and (3), it is concluded that, d‴(x)=a(x),d″(x)=b(x) and d′(x)=c(x)

Thus, d=f, c=f′, b=f″ and a=f‴.