Derivative Rules
Trig Derivatives
Something about f, f’, f”
Analyzing Functions and More
Calculus Fun Facts
100
What is the product rule?
f'g+g'f
100
Derivative of sinx
cosx
100
What does the graph of the derivative describe?
It shows all the slopes of lines tangent to the original graph
100
F(x)= 2x3-3x2-12x+18, when is the graph decreasing and concave up?
(-1, .5)
100
What is the name of that guy who made the rule about limits that are 0/0
lhopital
200
What is the quotient rule?
f'g-g'f/ g2
200
Derivative of tanx
sec2x
200
What does it mean when f'(x)= 0
A maximum, minimum, or horizontal tangent
200
If f(x)= x2-4, and g is a differentiable function of x, what is the derivative of f(g(x))
2g'(x)
200
What are the 2 big ideas of Calculus?
Slope and Area
300
What is the derivative of ax?
ax x ln(a)
300
Derivative of cscx
-cscxcotx
300
How do you decided whether a critical point is a maximum or minimum?
Positive to negative = max; negative to positive =min
300
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)
300
What should you use to wipe your calculus tears?
Toilet Paper
400
What is the derivative of logax?
1/x times 1/x
400
Derivative of tan(lnx)
sec2(lnx)/x
400
What does it mean when f''(x)= 0
Function can have a point of inflection there,
400
The limit does not exist
400
Why is the derivative of x equal to 1?
the line y=x, the slope is always one
500
Write the chain rule
(f’ º g) × g’
500
Derivative of 3sin(secx)
3cos(secx)tanxsecx
500
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
500
What is wrong with this response:
“The function has a relative max because it changes from positive to negative”
Who is “it”?
500
Is statistics real math?
no