# How do you find the tangent line to #y = x^2 + 3x - 4#?

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To find the tangent line to the equation y = x^2 + 3x - 4, we need to find the derivative of the equation. The derivative of y = x^2 + 3x - 4 is dy/dx = 2x + 3.

Next, we need to find the slope of the tangent line at a specific point. Let's say we want to find the tangent line at x = 2. We substitute x = 2 into the derivative equation: dy/dx = 2(2) + 3 = 7.

So, the slope of the tangent line at x = 2 is 7.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the point (2, y), we have y - y1 = 7(x - 2). Simplifying, we get y - y1 = 7x - 14.

Therefore, the equation of the tangent line to y = x^2 + 3x - 4 at x = 2 is y = 7x - 14.

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