Properties, rules, theorems, etc..
Name of the following rule...
f'(x)g(x)+ f(x)g'(x)
product rule
Evaluate
∫ 12x dx
6x2 + C
A function that models the slope of the curve for all x-values for which it exists. This is the definition of what?
The definition of a derivative
What's the volume of a cylinder?
V=πr2h
A function fails to be differentiable if it has a....
Discontinuity, corner, cusp or a vertical tangent
Name of the following rule...
d/dx= nx(n-1)
power rule
Evaluate
∫ x3-3x2 dx
x4/4 - x3 + C
Find the derivative of:
y=3x2
y'= 6x
What's the volume of a cone?
V=πr2(h/3)
What's the name of the guy who made the rule about limits that are 0/0
L'hopital
Name of the following rule...
d/dx = (f'(X) * g(X) − g’(X)* f(X) )/g^2
quotient rule
Evaluate
∫ 2x5−6x3+7x−4 dx
x6/3 - 3x4/2 + 7x2/2 - 4x + C
Find the derivative of:
2x3 + 6x2 + 5x + 3
6x2 + 12x + 5
What's the volume of a sphere?
V = 4/3πr3
The graph of a function f is concave down when f′ is decreasing. That means as one looks at a concave down graph from left to right, the slopes of the tangent lines will be decreasing.
Name of the following rule...
F'(x)= f’(g(x))g’(x)
chain rule
Evaluate
∫ (t2−1)(4+3t)dt
3/4t4 + 4/3t3 − 32t2 − 4t +C
Find the derivative of:
y=(3x2+16)4
y'=24x(3x2+16)3
You would integrate a function to find the ___ under the curve.
area
What is an inflection point?
A point of inflection is found where the graph of a function changes concavity.
What theorem states...
If f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c) =k
Intermediate Value theorem
Evaluate
∫ z7−48z11−5z16 dz
1/8z8 − 4z12 − 5/17z17 + C
Find the derivative of:
g(t)=(4t2−3t+2)-2
−2(8t−3)(4t2−3t+2)-3
Find the area enclosed by y=x2 and the y-axis between [0,3] is revolved around the y-axis.
9/2 π
To find the acceleration of a particle, which derivative of a function would you find?
The second derivative