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Calculus 4E-Ch 12&13

C4E - Ch 12: The Derivative & Ch 13: Finding More Derivatives

QuestionAnswer
The process for calculating speed was called the Method of ________________________. Increments
The 3 central concepts of calculus are the limit, the derivative, and the integral.
We use the word DERIVATIVE because we _____________ one function from another. derive
The INDEPENDENT variable is the ____________ of the function. input
The DEPENDENT variable is the ____________ of the function. output
The DEPENDENT variable is called so because its value ___________ upon the input. depends
In d(t), the INDEPENDENT variable is _____. Thus the DISTANCE that a falling objects travels depends on the TIME the object has been falling. t
A DERIVATIVE is the limit of the rate of change in the DEPENDENT variable with respect to the INDEPENDENT variable as the change in the independent variable approaches 0.
"The average rate of change in y with respect to x" is notated as: Δ y/Δ x
All derivatives ARE limits, but not all limits are ____________________. derivatives
The general form of quadratic functions: y(x) = ax^2 + bx + c
Quadratic functions can also be called: polynomials or second order polynomials.
"Quadratic" comes from the Latin word for square. We use it to describe quadratic functions because the highest exponent involved is a squared polynomial (exponent of 2).
The derivative of any function of the form y(x) = ax^2 is y'(x) = 2ax
"bx" is called a first-order term because the highest exponent is ____. 1
If a function has a derivative that is a constant, it does NOT mean that it is NOT changing; rather it means that it is changing _______________________. uniformly
The FIRST derivative o f y(x) = ax^2 + bx +c is y'(x) = 2ac +b
The SECOND derivative o f y(x) = ax^2 + bx +c is y"(x) = 2a
The THIRD derivative o f y(x) = ax^2 + bx +c is y'"(x) = 0
Created by: MrsHough
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