How to Calculate the Slope of a Curve

Slope
••• Wikimedia Commons,http://commons.wikimedia.org/wiki/File:Slope_picture.svg

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.

Related Articles

How to Find Equations of Tangent Lines
How to Integrate the Cube Root of X
How to Classify Polynomials by Degree
How to Solve a Parabola
How to Find the X Intercept of a Function
How to Find Derivatives
How to Calculate a Horizontal Tangent Line
How to Linearize a Power Function
How to Program a TI 83 Plus Calculator to Solve Rational...
How to Find X-Intercept & Y-Intercept
How to Calculate Stream Power
How to Simplify Monomials
How to Find the Slope & the Equation of the Tangent...
How to Convert Slope Intercept Form to Standard Form
How to Find a Tangent Line to a Curve
How to Convert From a Standard to a Vertex Form
How to Find the Slope in a Circle
Differences Between Quadratic & Linear Equations
How to Solve Large Exponents
How to Figure Out the Slope of a Line