Anti Derivative
Implicit Differentiation
Critical Points
Definite Intergrals
Miscellaneous
200
The Derivative of the function is F'(x)= 1/x^2.
What is
-2/x^3+c
200
A student sees an equation where y cannot be isolated easily, but y still depends on x.
What does this relationship between x and y represent?
What is a function defined implicitly?
200
Question: What is a critical point of a function?
What is a point where f '(x) = 0 or f '(x) is undefined?
200
Evaulate
∫_0^2 x dx
What is 2 ?
200
What does the second derivative of a function tell us?
What is the concavity?
400
The derivative of the Function
f'(x) 4x sin(x)
What is
4sin(x) + 4xcos(x)
400
Differentiate implicitly
x² + xy + y² = 7
What is dy/dx
(-2x - y)/(x + 2y)?
400
f'<0, f''>0. f'<0, f''<0. f'>0, f''> 0. f'>0, f''<0
What is
f'>0, f''>0
400
Evaluate the definite integral
∫ _0 ^ π sin(x) dx
What is 2
400
What is the limit of
(sin x)/x
as x approaches 0?
What is 1?
600
The Derivative of the Function is
f(x)= 6/x^3 - 6/x^7
what is
-3/x^2+1/x^6
600
With respect to x
x^2+y^2 =25 \text{ Find } dy/dx
What is
-x/y
600
Find the critical points of
f(x) = x³ − 3x
What are
x = −1 and x = 1?
600
Evaluate the definite integral
∫ _-3 ^3 √(9 − x²) dx.
9/2 pi
What is
600
Question: What is the slope of the tangent to sin(x) at x = π?
What is −1?
800
the Derivative of the function is
∫ x/sqrt(1+x^2) dx
What is
sqrt(1+x^2)+c
800
The given is
sin(xy) = x
What is
dy/dx = [1 - y*cos(xy)] / [x*cos(xy)]?
800
Find and classify the critical points of
f(x) = x² − 4x + 3
What is a minimum at x = 2?
800
DAILY DOUBLE
What is 9
800
An engineer designs a new bottle by rotating the curve of its side around a central axis to create a 3D shape. She wants to calculate how much liquid the bottle can hold. What type of calculus concept should she use to find the volume of the bottle?
What is the volume of a solid of revolution?