Math Problem Statement

f(x)=xxf\left(x\right)=x\sqrt{x}

Solution

The function you've provided is:

f(x)=xx=xx1/2=x3/2f(x) = x \sqrt{x} = x \cdot x^{1/2} = x^{3/2}

This can be simplified as:

f(x)=x3/2f(x) = x^{3/2}

Would you like to analyze or explore any specific aspects of this function (like derivatives, integrals, etc.)? Here are some possible directions we can explore:

  1. What is the derivative of f(x)=x3/2f(x) = x^{3/2}?
  2. What is the integral of f(x)=x3/2f(x) = x^{3/2}?
  3. What is the behavior of f(x)f(x) as xx \to \infty?
  4. What is the behavior of f(x)f(x) as x0x \to 0?
  5. Can we find any critical points or extrema for this function?

Tip: When dealing with fractional exponents, remember that xax^a can be interpreted as the function xx raised to a power aa, and this helps in both differentiation and integration.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Functions

Formulas

f(x) = x\sqrt{x} = x^{3/2}

Theorems

Exponent Rules: a^(m/n) = n-th root of (a^m)

Suitable Grade Level

Grades 9-12