Only gives me one critical point how do I get

I differentiated it and used solve to get it but I only get one critical point which is zero however when I go on desmos there should be more than one

Answer 1

[Birdman]

You may first see the roots graphically as follows:

t=-50:0.1:105;
plot(t,fun(t),t,fun(t)==0,'b--o')

Then, following lines will give you the roots.

fun=@(t) (2.13)*t.^2-(0.0013)*t.^4+(0.000034)*t.^(4.751);
sol=fzero(fun,x0);

Note that x0 component will be decided according to the graph. You need to write a value where x0 is close to the root of the equation. When you plot, you will decide those values. For instance, to find the value near 63, you may write

sol=fzero(fun,65)

value near 100, you may write

sol=fzero(fun,100);

The principle goes like this.

[Lamba Opa]

How would I differentiate the function first? diff(fun) seems to not work

[Birdman]

First, symbolically take diff:

syms t
eq=diff((2.13)*t.^2-(0.0013)*t.^4+(0.000034)*t.^(4.751),t);

Then, clear everything, write eq again into the structure above and make calculations.