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

  • calculus -

    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

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