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Popular >

monotone f(x)=x^{(5/3)}-x

Solution

monotone intervals

f (x) = x^{(\frac{5}{3})} - x

Solution

Increasing : - \infty < x < - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}}, Decreasing : - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}}, Increasing : \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \infty

Solution steps

f^{'} (x) = \frac{5 x ^{\frac{2}{3}}}{3} - 1

Find intervals:

Increasing

: - \infty < x < - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}},

Decreasing

: - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}},

Increasing

: \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \infty

Increasing : - \infty < x < - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}}, Decreasing : - \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}}, Increasing : \frac{3 \cdot 3 ^{\frac{1}{2}}}{5 \cdot 5 ^{\frac{1}{2}}} < x < \infty

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Frequently Asked Questions (FAQ)

What is the monotone f(x)=x^{(5/3)}-x ?
The monotone f(x)=x^{(5/3)}-x is