Question

Use MuPAD to determine all the local minima and local maxima and all the inflection points where dy/dx = 0 of the following function:

 

Answer 1

It is required to find the points where the differentiation of the function is zero.

y = x4 – 16/3 x3 + 8x2 - 4

 

The differentiation can be found using the MATLAB command diff and root can be calculated using the MATLAB command solve.

 

The MATLAB code is given below. After solving for differentiation of the function, we use the subs command to calculate the function value.

 

Input:

syms x

Y = x^4 - (16/3)*x^3 + 8*x^2 - 4;

d = diff(Y);

sol = solve(d)

points = subs(Y, sol)

 

Output:

 

Therefore, the points where the differentiation is zero are:

(x, y) = (0, -4), (2, 4/3).

 

The minimum is at (0, -4) and the inflection point is at (2, 4/3).

The minimum is at (0, -4) and the inflection point is at (2, 4/3).