prove that the function

Question

f(x) = (x^101)+(x^51)+x+1
has neither a local maximum nor a local minimum

Answer 1

Find the derivative of f(x) which gives you f'(x). Set f'(x)=0
this will give you the critical values. and you use those to find the max and min.

F'(x)= 101x^100 + 51x^50 + 1

0= 101x^100 + 51x^50 +1

the easiest way to find the critical numbers would be to use the quadratic formula