What is the number of points of intersection of the curves ?
For the next two (02) items that follow : Consider the curves \( y = x^2 \) and \( y = 2|x| \).
- A. 4
- B. 3 ✓
- C. 2
- D. None
Correct Answer: B. 3
Explanation
Equating the curves: \( x^2 = 2|x| \implies |x|^2 - 2|x| = 0 \). This gives \( |x|(|x| - 2) = 0 \), yielding |x| = 0 and |x| = 2. Thus, the x-coordinates are 0, 2, and -2, resulting in 3 points of intersection.
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?