Finding the equation of a tangent line to a curve

By Tutor GuyNo Comments

 

Finding the equation of a line that’s tangent to a function at a given point is not nearly as hard as it sounds. Think about what you need to write the equation of a line: a point and a slope. That’s all. Well, you’ve already been given the point. [If you don’t have the y-coordinate, just plug the x-coordinate into the function.] To find the slope, just take the derivative at the given value of x.

Example: Find the equation of the line tangent to the curve

when x = 4.

 

Solution: To find an equation for a line, you need a point and a slope. The tangent line touches the curve, so find the y-coordinate of the point on the curve when x = 4.

so the point is (4, 2). Now find the slope by finding the derivative at x = 4:

Now use the point-slope form to write the equation of the line:

Calculus
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