Chapter 3.5, Problem 67E

Solution

a.

To graph: Graph the function $f\left(x\right)=k·e^{–c{x}^2}$ , where $c$ and $k$ are positive constants is a bell-shaped curve that is useful in probability and statistics. Explain the effect of changing.

Given information: The function $f\left(x\right)=k·e^{–c{x}^2}$ .

Graph:

The given function is- $f\left(x\right)=k·e^{–c{x}^2}$ ;

By substitute few values of $c$ and $k$ in function, $f\left(x\right)=k·e^{–c{x}^2}$ .

  $c=1$ and $k=0.1,0.5,1,2,10$ ;

  

Interpretation:

The graph grows ‘taller’ as $k$ increase.

b.

To graph: Graph the function $f\left(x\right)=k·e^{–c{x}^2}$ , where $c$ and $k$ are positive constants is a bell-shaped curve that is useful in probability and statistics. Explain the effect of changing.

Given information:

The function $f\left(x\right)=k·e^{–c{x}^2}$ .

Graph:

The given function is- $f\left(x\right)=k·e^{–c{x}^2}$ , By substitute few values of $c$ and $k$ in function, $f\left(x\right)=k·e^{–c{x}^2}$ .

  $k=1$ and $\text{c}=0.1,0.5,1,2,10$ ;

  

Interpretation:

The smaller $c$ is, the wider the graph will be.