What is the <strong>MAXIMUM</strong> value of xy?
Consider the following for the next two (02) items that follow: Given that 4x^{2}+y^{2}=9.
- A. \frac{9}{4} ✓
- B. \frac{3}{2}
- C. \frac{4}{9}
- D. \frac{2}{3}
Correct Answer: A. \frac{9}{4}
Explanation
We can use the AM-GM inequality on the positive terms 4x^2 and y^2: \frac{4x^2 + y^2}{2} \geq \sqrt{4x^2 y^2}. Substituting 4x^2 + y^2 = 9, we get \frac{9}{2} \geq 2|xy| \implies |xy| \leq \frac{9}{4}. Therefore, the maximum value of xy is \frac{9}{4}.
Related questions on Calculus
- Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
- If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
- What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
- What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?