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

1 Answer
Jan 3, 2015

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.