Unit 1
What are the 3 factors of a continuous function?
Value has to be defined, Limit has to exist, and the defined number/limit have to equal each other.
What are the 4 types of rules we use to find the derivative of the function?
Chain, power, quotient, and product
If the second derivative is positive, then the original function...
Is concave up
What is the definition of optimization?
maximize a quantity, take derivative of function = 0 = critical points. first deriv test to max or min.
What does a differential equation need to have?
A derivative of y
What are the three types of discontinuities in a function?
Removal, jump, and infinite
What quote do we use every time we use quotient rule?
“Low di High - High di Low, Square the bottom
and off you go"
If the velocity is negative and the acceleration is also negative, then the speed is...
Increasing
What is the equation of a constraint?
X + Y = S (sum) Constraint Equation
How do you find the particular solution?
First you should find the antiderivative of the function. Then you substitute the initial condition to find C (constnat of integration). Then you substitute the x value to the equation to get the answer.
What do you have to do when you are trying to solve for a limit that is a vertical asymptote?
Sign test
What technique do we use when we are funding the derivative with multiple variables?
Implicit differentiation
When do you use L'Hopital's Rule?
When you get an indeterminate number (0/0)
How do you find the absolute minimum/maximum of a function?
Find the critical points plus the endpoints. Then plug those values to the original function to get the answer.
what steps we should use for slope fields?
Evaluate the differential equation at various points (x,y)
sketch a line segment with the slope
If the degree of a numerator is greater than a denominator, the horizontal asymptote...
does not exist
What is the derivative of the inverse of cosine?
-1/sqrt(1-x^2)
What is the relationship between tangent line approximation and normal line approximation?
normal line approxiamtion is the opposite reciprocal of the tangent approxiamtion (in terms of the slope).
What is the equation for optimization?
XY = P (product) Optimization equation
General solutions include a (+c). true or false?
FALSE
If x=0 has a jump discontinuity, then...
the limit does not exist and x=0 is the horizontal asymptote.
What is the Mean Value Theorem?
The average rate of change over an interval is equivalent to the instantaneous rate of change at least at one point over the interval
Velocity is the derivative of acceleration. (true or false)
FALSE
What are the 4 types of theorems we utilized in unit 5?
Extreme Value thoerem, Mean value theorem, Intermidiate Value theorem, and fundamental thoerem
what is the antiderivative of dy/dx=Ky
Y=Ce^kt