How do you find the slope and tangent line to the curve #y=6-x^2# at x=7?
Slope
equation:
To find the slope you need to derive your function and evaluate the derivative at at To find the equation of the tangent line you need also the value of Graphicall (the red line is the tangent):
deriving:
So basically your tangent has solpe
Now use the relationship:
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To find the slope of the curve at a specific point, we need to find the derivative of the function. The derivative of y=6-x^2 is dy/dx = -2x.
To find the slope at x=7, we substitute x=7 into the derivative: dy/dx = -2(7) = -14.
Therefore, the slope of the curve at x=7 is -14.
To find the equation of the tangent line at x=7, we use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the point on the curve.
Substituting x=7, y=6-7^2=-43 into the equation, we have: y - (-43) = -14(x - 7).
Simplifying, we get the equation of the tangent line: y = -14x + 105.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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