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 $latex f(x)=3{{x}^{2}}-4x+1$.

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

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

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

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

- 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.