# How do you find the slope of the tangent line to the curve #y=x-x^2# at (1,0)?

the slope is 1-2x

to get to the slope of the function you'll need to differentiate. ie d/dx (x-x^2) is 1-2x, this is the slope of the function but also the slope of the tangent line since they are equal.

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To find the slope of the tangent line to the curve (y = x - x^2) at the point ((1, 0)), we first need to find the derivative of the function (y) with respect to (x). Then, we evaluate the derivative at (x = 1) to find the slope of the tangent line at that point.

The derivative of (y = x - x^2) with respect to (x) is given by (y' = 1 - 2x).

Now, evaluate (y') at (x = 1): [y'(1) = 1 - 2(1) = 1 - 2 = -1.]

So, the slope of the tangent line to the curve (y = x - x^2) at the point ((1, 0)) is (-1).

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