Chapter 8, Problem 1P

To determine

To plot:

The polynomial $y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ in the domain $-6\le x\le 6$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

Answer to Problem 1P

Solution:

The plot of the given polynomial $y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ is stated as follows.

Explanation of Solution

The given polynomial function is,

$y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ …… (1)

The range of the function is $-6\le x\le 6$.

Substitute the value of $x=-6$ in the above equation.

$\begin{array}{c}y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235\\ =0.1{\left(-6\right)}^5-0.2{\left(-6\right)}^4-{\left(-6\right)}^3+5{\left(-6\right)}^2-41.5\left(-6\right)+235\\ =-\text{156}\text{.8000}\end{array}$

Substitute the value of $x=6$ in equation (1).

$\begin{array}{c}y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235\\ =0.1{\left(6\right)}^5-0.2{\left(6\right)}^4-{\left(6\right)}^3+5{\left(6\right)}^2-41.5\left(6\right)+235\\ =\text{468}\text{.4000}\end{array}$

Hence, the value of $y$ lies from $-\text{156}\text{.8000}\le y\le \text{468}\text{.4000}$.

Write the MATLAB script to plot the polynomial $y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ in the domain $-6\le x\le 6$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

MATLAB Code:

%MATLAB program to plot the polynomial function

x = -6:0.1:6;%Define a vector x.

y = [0.1 -0.2 -1 5 -41.5 235];

r = polyval(y,x);%polyval function is used to calculate y

plot(x,r)

xlabel('x')

ylabel('y')

Save the MATLAB script with the name, Chapter8_29864_8_1P.m in the current folder. Execute the script by typing the script name at the command window to get the plot of the polynomial $y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ in the domain $-6\le x\le 6$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

Result:

Conclusion:

Therefore, the plot of the given polynomial $y=0.1x^5-0.2x^4-x^3+5x^2-41.5x+235$ is stated above.