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The acute angles between the curves y=2x...

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

A

`alpha-beta=0`

B

`alpha+beta=0`

C

`alpha gt beta`

D

`alpha lt beta`

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The correct Answer is:
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 first curve \( y = 2x^2 - x \): \[ \frac{dy}{dx} = \frac{d}{dx}(2x^2 - x) = 4x - 1 \] 2. For the second curve \( y^2 = x \): \[ 2y \frac{dy}{dx} = 1 \implies \frac{dy}{dx} = \frac{1}{2y} \]
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