Calculus 1 : Meaning of Functions
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #61 : Meaning Of Functions
Find the slope of the tangent line equation for 
To find the slope, we need to differentiate the given function. By product rule and chain rule, we have 
Example Question #61 : Meaning Of Functions
Function
What is a function?
A function is a relationship that assigns to each input value a single output value
None of the above
A function is an equation with at least two unknowns such as x and y
A function is a matematical equation with one or, more variables
A function is a relationship that can produce multiple output values for each single input value
A function is a relationship that assigns to each input value a single output value
You could think of a function as a machine that takes in some number, performs an operation on it, and then spits out another number
Example Question #62 : Meaning Of Functions
Identify Function
Which one of the following is not a function?
For any value of 
Example Question #63 : Meaning Of Functions
Type of Functions
What type of function is this:
Piecewise
Quadratic
Linear
Polynomial
Rational
Piecewise
Piecewise functions are a special type function in which the formula changes for different 
Example Question #64 : Meaning Of Functions
Find the domain of the function
Example Question #66 : How To Find The Meaning Of Functions
What is the slope of this curve at 
To find the slope of a curve at a certain point, you must first find the derivative of that curve.
The derivative of this curve is 
Then, plug in 
Example Question #67 : How To Find The Meaning Of Functions
What are the critical points of 
To find the critical points of a function, you need to first find the derivative and then set that equal to 0. To find the derivative, multiply the exponent by the leading coefficient and then subtract 1 from the exponent. Therefore, the derivative is 
Example Question #64 : Meaning Of Functions
Finding when the second derivative is positive tells us what about a function?
When the function is concave down.
When the function is concave up.
When the function is decreasing.
When the function is increasing.
When the function is concave up.
The first derivative of a function tells us about the slope and the second derivative tells us about concavity. Thus, when the second derivative is positive, it tell us that the concavity is upward. Therefore, a postive second derivative means the function is concave up.
Example Question #69 : How To Find The Meaning Of Functions
Given the position function below, what does evaluating it at 
It tells us that at 
It tells us that at 
It cannot be determined.
It tells us that at 
It tells us that at
When asked to evaluate the function, you must realize that you are going to be plugging in a value for t. Therefore, we need to figure out what the output value is telling us when t=1. Since we are simply given the position function, adn now asked to integrate it or differentiate it, our output will simply tell us the position of our object when t=1. Thus,
Example Question #65 : Meaning Of Functions
Evaluate the following limit:
Does not exist.
When evaluating the limit through direct substitution, one ends with the indeterimate form 0/0, therefore another approach must be followed. Two approaches would work here:
1.
One could use L'Hospital's Rule, which states that if a function is indeterminate when evaluating, one should then take the derivative of the top function over the derivative of the bottom.
In this case one would find
2.
Alternatively, one could simply factor both the numerator and the denomenator, removing common factors.
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