Tangent slope is limiting value of secant slope

The  exercise appears under the Differential calculus Math Mission. This exercise uses the slopes of secant lines to understand the slope of a tangent line.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the derivative (essentially): This problem provides an expression which is really just the derivative. The student is asked to select the expression that correctly represents what they are trying to calculate.Tsilvoss1.png
 * 2) Fill in the values: This problem provides a grid of inputs and outputs for a particular function. The student is expected to fill in the specific answers and use them to find the answer to the overall limit.Tsilvoss2.png
 * 3) Calculate the requested amount: This problem provides some values and expressions. The student is expected to use the provided information to find the answer to an intensive request based on the information.Tsilvoss3.png

Strategies
Knowledge of the graphs of functions, their derivatives, and their antiderivatives are encouraged to ensure success on this exercise.
 * 1) A derivative is positive when a function is increasing, and a function is negative when the function is decreasing.

Real-life Applications

 * 1) Calculus has massive applications to physics, chemistry, biology, economics and many other fields.
 * 2) The slope of a curve is the natural extension of a linear slope.