How to Calculate the Slope of a Curve

By Kaitlyn Yeager; Updated April 24, 2017

To calculate the slope of a curve, you need to calculate the derivative of the curve's function. The derivative is the equation of the slope of the line tangent to the point on the curve whose slope you want to calculate. It is the limit of the curve's equation as it approaches the indicated point. There are several methods for calculating the derivative, but the power rule is the simplest method and can be used for most basic polynomial equations.

Write out the equation of the curve. For this example, the equation 3X^2 + 4X + 6 = 0 will be used.

Cross out any constants in the original equation. A slope is a rate of change, and because constants do not change, their slope equals 0, and so they will not be present in the derivative.

Bring the power of each X term down in front of the term as a multiplier, and subtract one from the original power to get the new power. So, the 3X^2 from the example becomes 2(3X^1), or 6X, and the 4X becomes 4. These two steps are the basics of the power rule. The sample derivative equation now reads 6X + 4 = 0.

Choose the point of the original curve whose slope you would like to calculate, and plug the X coordinate into the derivative equation to get the slope value. In the example, the slope at the point (1,16) would be 10.

About the Author

Kaitlyn Yeager is a newspaper web producer Connecticut and has been working in journalism since 2006. She graduated with a Bachelor of Arts in journalism in 2009. Yeager enjoys sharing information about knitting and crocheting, her two main hobbies.