How do you find the equation of the tangent line to the curve #y=3x^2-x^3# at point (1,2)?
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To find the equation of the tangent line to the curve y=3x^2-x^3 at point (1,2), we need to find the slope of the tangent line at that point.
First, we find the derivative of the function y=3x^2-x^3 with respect to x.
The derivative is given by dy/dx = 6x - 3x^2.
Next, we substitute x=1 into the derivative to find the slope at the point (1,2).
dy/dx = 6(1) - 3(1)^2 = 6 - 3 = 3.
Therefore, the slope of the tangent line at point (1,2) is 3.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we substitute the values into the equation.
y - 2 = 3(x - 1).
Simplifying the equation, we get y - 2 = 3x - 3.
Finally, rearranging the equation, we have y = 3x - 1.
Therefore, the equation of the tangent line to the curve y=3x^2-x^3 at point (1,2) is y = 3x - 1.
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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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