Final Exam Flashcards
(18 cards)
How do you find a limit as it is approaching “c”?
Plug c into the equation if it is undefined, you have to factor out something in the denominator, then plug c back in
How do you know what side the limit is being approached from?
If there is a negative sign then the limit is being approached from the left side(negative side)
If there is a positive sign then the limit is being approached from the right side(positive side)
If a limit is approaching infinity or negative infinity what are you looking for?
A horizontal asymptote
What things are required for a function to be continuous?
-The limit will exist
- Y-value exists
- The limit and y-value have to equal one another
How do you find the slope of a line tangent to a graph?
Find the derivative of the function, then plug the x-value in to get the slope
How do related rates work?
Translate- Figure out what you are solving for
Relate variables- write down all variables and the equation you will be finding the derivative of
Relate the rates and answer question- now solve by plugging things in and solving for what you said in step 1
How do you find the instantaneous rate of change?
Find the second derivative of the function
Critical points
a point where the function’s derivative is either zero or undefined
Mean Value Theorem
For a continuous and differentiable function over a closed interval, there exists a point within that interval where the instantaneous rate of change (derivative) equals the average rate of change(slope) over the interval
Average rate of change vs instantenous rate of change
Average rate of change considers the change over an entire interval, while instantaneous rate of change focuses on the change at a specific point in time.
Intermediate Value Theorem
if there is a continuous function whose domain contains the interval [a, b], then it takes on any given value within the interval.
If you are shown a graph of a derivative(f’) then what do you know about concavity?
If f’ is decreasing, then f’’ is concave down, and the opposite if it is increasing
What does concave up or down mean when related to the original function?
f”(x) >0 is concave up and f”(x) < 0 is concave down
How do you know if the original function is increasing or decreasing according to the original function?
Find the derivative of the function and when the function is negative it is decreasing when it is positive it is increasing
How do you find relative or absolute extrema?
It is when f’(x)=0
It asked to find the absolute extrema when given a function how do you find it?
Find the derivative of the function, and find the zeros of the derivative.
Then, use the zeros and the endpoints and plug them into the ORIGINAL function and whichever one has the highest or lowest number is your absolute extrema
What is a quick way to find a horizontal asymptote with a rational function?
If the x in the numerator and the denominator are in the same degree(both x^2, x^4, etc.) then you divide them and whatever you get is where the HORIZONTAL asymptote will be
How do you find the antiderivative of something when you have to use substitution and you need to plug in two values?
You plug the two values into whatever you make “u”. Then you solve the antiderivative as normal just plug your two new values in.
