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The curves y=4x^(2)+2x-8 and y=x^(3)-x+1...

The curves `y=4x^(2)+2x-8` and `y=x^(3)-x+13` touch each other at which point?

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To find the point where the curves \( y = 4x^2 + 2x - 8 \) and \( y = x^3 - x + 13 \) touch each other, we need to follow these steps: ### Step 1: Find the derivatives of both curves First, we differentiate both equations to find the slopes of the tangents to the curves. For the first curve \( y = 4x^2 + 2x - 8 \): \[ \frac{dy}{dx} = \frac{d}{dx}(4x^2 + 2x - 8) = 8x + 2 ...
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