Rules of Differentiation
The derivative of any constant.
What is the value a function approaches as its input gets closer and closer to a specific number?
The derivative of e^x
What is e^x?
The process of finding the maximum or minimum value of a function, subject to given constraints
What is Optimization?
Gives us the area under the curve of that function
What is the definite integral?
The derivative of two functions being multiplied to one another.
What is the derivative of the first function times the second, plus the first function times the derivative of the second?
What is continuity?
a function whose graph is a smooth, unbroken line that you can trace without lifting your pencil
Find the derivative of
πβ‘(π₯) =6β’π₯^3 β9β’π₯ +4
What is 18β’π₯^2β9?
Finding the rate at which a quantity changes by using known information about the rate of change of another related quantity.
What are Related Rates?
Also known as an antiderivative.
What is an indefinite integral?
The derivative of two functions being divided.
What is (Differentiation of 1st function Γ the 2nd function β Differentiation of second function Γ the 1st function) to the square of the 2nd function.
If the point on a graph is hollow (e.x. like the letter o) and it falls on the function, is it continuous?
No
The derivative of ln(x)
What is 1/x?
Lucky you, free 300 Points
Lol
A simple calculus method used to approximate the total area under a curve by dividing the region into simple geometric shapes like rectangles
What are Riemann Sums?
How one would differentiate a composite function.
What is differentiating the outer function and multiplying it by the derivative of the inner function.
Solve:
lim π‘ββ3
6+4β’π‘/π‘^2+1
What is -3/5
What is cos(x)?
We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft. If we have $700 determine the dimensions of the field that will maximize the enclosed area.
x = 350/9
y = 35/2
Used to measure the space bounded by a function f(x), the x-axis, and specified boundary lines.
What is the area under the curve?
The derivative of a function with sin(x).
What is cos(x)
Solve:
limπ₯β2β‘(8β3β’π₯+12β’π₯^2)
Find the Derivative of
ββ‘(π¦) =π¦^β4 β9β’π¦^β3 +8β’π¦^β2 +12
What is
4β’π¦^β5 + 27β’π¦^β4 β16β’π¦^β3
In the following assume that π₯ and π¦ are both functions of π‘. Given π₯ =β2, π¦ =1 and π₯β² =β4 determine π¦β² for the following equation.
6β’π¦^2 + π₯^2 = 2βπ₯^3β’π^(4β4β’π¦)
y' = 8/11