Differentiating a function and finding critical points

I have been set a problem and managed to complete the first part which was to plot the function:

y= t^6-4*t^4-2*t^3+3*t^2+2*t

This was done in the Editor as a script: %script file to plot (y =f(t)= t^6-4*t^4-2*t^3+3*t^2+2*t) %interval [-3/2:5/2] t =[-3/2:0.01:5/2]; y=t.^6-4*t.^4-2*t.^3+3*t.^2+2.*t; plot (t,y)

But now I have to differentiate this function to find where f'(t) = 0...

In the command window, I typed diff(y), which gives a list of values. However, I am not sure how to use fzero to find the critical points.

Answer 1

[Mischa Kim]

Will, you could work symbolically to get the job done:

 syms y t
 y  = t^6 - 4*t^4 - 2*t^3 + 3*t^2 + 2*t;
 dy = diff(y,t)
 dy =
   6*t^5 - 16*t^3 - 6*t^2 + 6*t + 2
 rootsdy = double(solve(dy == 0))
 rootsdy =
  -1.000000000000000
  -1.000000000000000
   1.684694738462017
   0.629578614136595
  -0.314273352598613
 ezplot(y,[-1 2])
 grid