Definition: We know how to find the slope of the tangent line. By taking the derivative at a point, x, we can quite easily find an equation for a line tangent to a curve at a point . We will use the point-slope formula for a line, which you may recall from algebra. The equation for a line with slope m through a point is:
Example: Find the equation of a line tangent to the curve at the point .
Solution: First, we find the slope of the tangent line by taking the derivative at . Then, we use the point-slope equation to create a line equation:
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