## Calculus Tutorial

*Using Derivatives to Find the Slope at a Certain Point*

#### Intro

Say you have an equation that asks you to find the slope of a graph at the point x. How would you do this? Using Calculus, you would do this using derivatives. By taking the derivative of the given equation, you can plug in the point at which they want the slope and solve. Finding the slope of a graph at a particular point is a basic skill you will need if you want to excel in the rest of your calculus course.

#### Sample Problem

Using derivatives, find the slope of t^2+3t-1 at time t=4.

#### Solution

Step 1: Begin by rewriting your equation.

g(t)=t^2+3t-1

Step 2: Take the derivative

g(t)=t^2+3t-1

Becomes

g'(t)=2t+3

Step 3: Plug in the time they give you, which in this case is t=4

g'(4)=2(4)+3

Step 4: Simplify and Solve

g'(4)=8+3

g'(4)=11

The slope of the graph g(t) is 11 at time t=4

# About The Author

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Hello! My name is Alexandria Hodges and I am a current senior at the High School of Health Professions in downtown Dallas. Throughout my high school career I have earned and maintained high scores in all my courses and earned many awards for academic excellence including A Honor Roll and the DISD Sc... |

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