Derivative Rules
What is the product rule?
f'g+fg'
Derivative of sinx
cosx
What does the graph of the derivative describe?
It shows all the slopes of lines tangent to the original graph
F(x)= 2x3-3x2-12x+18, when is the graph decreasing and concave up?
(.5, 2)
What is the name of that guy who made the rule about limits that are 0/0
lhopital
What is the quotient rule?
f'g-fg'/ g2
Derivative of tanx
sec2x
What does it mean when f'(x)= 0
Horizontal tangent, possible extrema
If f(x)= x2-4, and g is a differentiable function of x, what is the derivative of f(g(x))
2g'(x)
What are the 2 big ideas of Calculus?
Slope and Area
What is the derivative of ax?
ax ln(a)
Derivative of cscx
-cscxcotx
How do you decided whether a critical point is a maximum or minimum?
Positive to negative = max; negative to positive =min
State the Mean Value Theorem
If a function is continuous on a closed interval [a,b] and differentiable on open interval (a,b), then there is a value c on (a, b) such that f’(c) =(f(b)-f(a))/(b-a)
What should you use to wipe your calculus tears?
Toilet Paper
What is the derivative of logax?
1/(xlna)
Derivative of tan(lnx)
sec2(lnx)/x
What does it mean when f''(x)= 0
Function can have a point of inflection there,
Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters. What is the radius of the one with maximum volume?
10/pi
Why is the derivative of x equal to 1?
the line y=x, the slope is always one
Write the chain rule
(f’(g)) × g’
Derivative of 3sin(secx)
3cos(secx)tanxsecx
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
What is wrong with this response:
“The function has a relative max because it changes from positive to negative”
Who is “it”?
Is statistics real math?
no