Question

How do I find extrema of `f(x) = x^7 - 14x^5 - 4x^3 - x^2 + 3` on a graphing calculator?

Answer 1

Fastest way would be to use the derivative function.

Whenever the derivative, also called the slope function reaches `0` you have reached a top or 'valley' of your original function.

You can find the derivative by remembering:

if `f(x)=a*x^n` then `f'(x)=n*a*x^(n-1)`

While numbers without `x` have a derivative of `0`

Going from there, the derivative of your function is:

`f'(x)=7*x^(7-1)-5*14x^(5-1)-3*4x^(3-1)-2*x^(2-1)+0`, or

`f'(x)=7x^6-70x^4-12x^2-2x`

Enter this in your GC as `Y1=`
Now, on your GC you go find the zeroe-values (there's a menu for that)
Since your equation is 7th grade (because of `x^7`) you may find as many as 6 zero points for the derivative (`x=0` is one of them).
Fill in these `x`'s in the original equation and you will have the co-ordinates of all extremes.