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

Please see the explanation.

Find the slope of the tangent line by computing the first derivative and then evaluate it at the desired x coordinate.

Compute the first derivative:

The desired x coordinate is 0, therefore the slope, m, is:

Use the point-slope form of the equation of a line:

The equation of the tangent line is:

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To find the equation of the line tangent to the curve y = -x^2 at the point (0,0), we can use the concept of differentiation.

First, we need to find the derivative of the function y = -x^2 with respect to x. The derivative of -x^2 is -2x.

Next, we substitute the x-coordinate of the given point (0,0) into the derivative to find the slope of the tangent line at that point. Since x = 0, the slope is -2(0) = 0.

Now, we have the slope of the tangent line, which is 0, and the point (0,0) that the line passes through. Using the point-slope form of a linear equation, y - y1 = m(x - x1), we can substitute the values to find the equation of the tangent line.

Substituting y1 = 0, x1 = 0, and m = 0 into the equation, we get y - 0 = 0(x - 0), which simplifies to y = 0.

Therefore, the equation of the line tangent to y = -x^2 at (0,0) is y = 0.

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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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