How Do You Find Where the Slope of the Tangent Line is Some Value?

A few of you had trouble with the problems referring to slopes of tangent lines. Remember, the slope of a tangent line to a function is given by the derivative. So by setting the derivative equal to the desired slope value, we can solve for the x value.

Problem 1 For the function f(x)=3{{x}^{2}}-4x+1.

    1. Find where the tangent line is horizontal.
    2. Find where the tangent line’s slope is equal to -1.

Problem 2 For the function f(x)=2{{x}^{2}}-5x+7.

    1. Find where the tangent line is horizontal.
    2. Find where the tangent line’s slope is equal to 1.

Problem 3 For the function f(x)=2{{x}^{3}}-11{{x}^{2}}-8x+1.

    1. Find where the tangent line is horizontal.

In this last example, you need to factor the quadratic to find the two places where the tangent line is horizontal (has a slope of zero). In some instances, you might need to use the quadratic formula to solve the equation.