Find the critical point of the following function. f(x)=x^(2/3)+2x^(−1/3)

mydaruma25

mydaruma25

Answered question

2022-09-23

Find the critical point of the following function.
f ( x ) = x 2 / 3 + 2 x 1 / 3

Answer & Explanation

Simeon Hester

Simeon Hester

Beginner2022-09-24Added 16 answers

f ( x ) = 2 3 x 1 / 3 2 3 x 4 / 3 = 2 3 ( x 1 / 3 x 4 / 3 ) = 2 3 ( x 3 / 3 x 4 / 3 x 4 / 3 ) = 2 3 x 4 / 3 ( x 3 / 3 1 ) = 2 3 x 4 / 3 ( x 1 ) = 2 ( x 1 ) 3 x 4 / 3 = 2 ( x 1 ) 3 x 4 3
Now, we have critical points where
f ( x ) is undefined: at x = 0, as is f ( x )
f ( x ) = 0 :: This will occur if and only when the numerator is zero. In this case, f ( x ) = 0 when ( x 1 ) = 0 x = 1.
Nathanael Perkins

Nathanael Perkins

Beginner2022-09-25Added 2 answers

Hint:
x 1 3 x 4 3 = x 4 3 1 3 = x x 0.

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