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Find the slope of the tangents to the curve y=−x2+5x−6

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Answer to a math question Find the slope of the tangents to the curve y=−x2+5x−6

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Maude
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To find the slope of the tangents to the curve at a particular point, we need to find the derivative of the function y with respect to x.

Given function: y = -x^2 + 5x - 6

Taking derivative of y with respect to x:

\frac{dy}{dx} = \frac{d}{dx} (-x^2 + 5x - 6)
\frac{dy}{dx} = -2x + 5

Now, this gives us the slope of the curve at any point on the curve. So, if we want to find the slope at a specific point, we need to substitute the x-coordinate of that point into the derivative expression.

Therefore, the slope of the tangent to the curve y = -x^2 + 5x - 6 at any point is \boxed{-2x + 5} .

Note: The slope of the tangent changes depending on the x-coordinate of the point on the curve, as given by the derivative of the function y.

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