Consider the curve given by the function f(x)=(x−1)2(1−2x)(x−2)
Find all critical points of f(x).
f′(x)=−(x−1)3x+1
I understand that critical points occur when f'(x)=0 or undefined.
derivative equal to zero:
I set f'(x) = 0, to get x=-1 (which is correct).
f′(x)=0=−(x−1)3x+1
0=−x−1
x=−1 (which is correct)
derivative is undefined:
I also have another critical point at x=1. If you let x = 1 in the function, then the denominator would be 0, and therefore the function is undefined....
(x−1)(x−1)(x−1)
x−1=0
x=1 (which is wrong)
But the answer key doesnt have this as their answer.
Find all critical points of f(x).
f′(x)=−(x−1)3x+1
I understand that critical points occur when f'(x)=0 or undefined.
derivative equal to zero:
I set f'(x) = 0, to get x=-1 (which is correct).
f′(x)=0=−(x−1)3x+1
0=−x−1
x=−1 (which is correct)
derivative is undefined:
I also have another critical point at x=1. If you let x = 1 in the function, then the denominator would be 0, and therefore the function is undefined....
(x−1)(x−1)(x−1)
x−1=0
x=1 (which is wrong)
But the answer key doesnt have this as their answer.
Last edited by a moderator: