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

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To find the equation of the line tangent to the graph of y = x^2 - 3 at the point P(2,1), we can use the concept of differentiation.

First, we differentiate the given function y = x^2 - 3 with respect to x to find its derivative.

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

Next, we substitute the x-coordinate of the point P(2,1) into the derivative to find the slope of the tangent line at that point.

Substituting x = 2 into dy/dx = 2x, we get the slope m = 2(2) = 4.

Now, we have the slope of the tangent line, and we also have a point on the line, P(2,1). We can use the point-slope form of a linear equation to find the equation of the tangent line.

Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point (2,1) and m is the slope 4, we substitute the values into the equation.

Therefore, the equation of the line tangent to the graph of y = x^2 - 3 at the point P(2,1) is y - 1 = 4(x - 2).

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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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