Question

Use MATLAB to plot the polynomial y = 3x⁴ - 5x³ - 28x² - 5x + 200 on the interval $1 ≤ x ≤ 1. Put a grid on the plot and use the ginput function to determine the coordinates of the peak of the curve.

 

 

Answer 1

We are required to plot the polynomial

y = 3x4 – 5x3 – 28x2 – 5x + 200

 

Over the interval

-1 ≤ x ≤ 1

 

We need to create a vector x and evaluate the polynomial at each element of vector x. We can use the function polyval(a, x) which is use to evaluate the polynomials. 

 

Here:

a is the polynomial array

x is the vector array

 

The below MATLAB code shows the commands

 

The plot generated is shown below:

 

Now, we use the ginput function to calculate the coordinates of the peak of the function. The command used is [x, y] = ginput. Then we need to click on the highest point and click enter. The results will appear on the screen. 

 

The output is shown below:

 

Hence, we get the coordinated of the peak of the curve as:

 

x = -0.0853

y = 200.2770

Hence, we get the coordinated of the peak of the curve as:

 

x = -0.0853

y = 200.2770