The acute angles between the curves `y=2x^(2)-x and y^(2)=x` at (0, 0) and (1, 1) are `alpha and beta` respectively, then

Options

A. `alpha-beta=0`
B. `alpha+beta=0`
C. `alpha gt beta`
D. `alpha lt beta`

Answer

To find the acute angles between the curves \( y = 2x^2 - x \) and \( y^2 = x \) at the points \( (0, 0) \) and \( (1, 1) \), we will follow these steps:

### Step 1: Find the derivatives of the curves

1. For the curve \( y = 2x^2 - x \):
\[ \frac{dy}{dx} = 4x - 1 \]

2. For the curve \( y^2 = x \):
Using implicit differentiation:
\[ 2y \frac{dy}{dx} = 1 \implies \frac{dy}{dx} = \frac{1}{2y} \]