Question

The angle between the curves y = x3 and y = x5 at x = 0 is

• A. \(\frac{\pi}{2}\)
• B. 0
• C. \(\frac{\pi}{3}\)
• D. \(\frac{\pi}{4}\)

Answer 1

The Correct Option is B

To find the angle between the curves, we need to find the angle between their tangents at the given point.
First, let's find the slope of the tangent (i.e., the derivative) for each curve at ( x = 0 ). 
For \(( y = x^3 ): [ \frac{dy}{dx} = 3x^2 ] At x = 0\)
\(( \frac{dy}{dx} = 0 ). For ( y = x^5 ): [ \frac{dy}{dx} = 5x^4 ] At ( x = 0 ), ( \frac{dy}{dx} = 0 ). \)
Both tangents are horizontal at x = 0
Therefore, the angle between them is ( 0 ) degrees or ( 0) radians. 
So, the correct answer is: 2. ( 0 )