How do you find the slope of the tangent line to a curve at a point?

Question

Charles Anctil · Accepted Answer

First take the given input value, x, and substitute it into the function to find the corresponding output value, y. You now have the point of tangency.

Second, find the expression that describes the derivative of the function by differentiation.

Third, substitute in the x value to find the slope/derivative of the tangent line.

Fourth, substitute in the x and y values from the point of tangency in step 1 into the slope intercept formula, y=mx+b. Now you can solve this equation for b, the y-intercept.

Fifth, substitute in the values of b and the slope/derivative in the slope intercept formula, y=mx+b, and you now have the equation of the tangent line at that specific point of tangency.

Please see the video example.

Video example

Adam Adkins · Answer

undefined To find the slope of the tangent line to a curve at a point, you can use the derivative of the function representing the curve. The derivative represents the rate of change of the function at any given point. To find the derivative, you can use differentiation rules or techniques such as the power rule, product rule, or chain rule. Once you have the derivative, evaluate it at the desired point to find the slope of the tangent line at that point.