# How do you find the equation of the line tangent to #y=3x^2-x^3# at point (1,2)?

distributing and simplifying gives an alternative version of the equation.

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To find the equation of the line tangent to the curve y=3x^2-x^3 at the point (1,2), we need to find the slope of the tangent line at that point.

To find the slope, we take the derivative of the given function y=3x^2-x^3 with respect to x.

The derivative of y=3x^2-x^3 is dy/dx = 6x - 3x^2.

Now, 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.

So, the slope of the tangent line at the 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 can substitute the values to find the equation of the tangent line.

Using (1,2) as the point and 3 as the slope, we have y - 2 = 3(x - 1).

Simplifying the equation, we get y - 2 = 3x - 3.

Rearranging the equation, we have y = 3x - 1.

Therefore, the equation of the line tangent to y=3x^2-x^3 at the 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.

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