Derivative Rules
What is the derivative of a constant?
0
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?
(-1, .5)
What phrase is this "C. O. V."
Change of Variables
What is the quotient rule?
f'g-g'f/ g2
Derivative of tanx
sec2x
What does it mean when f'(x)= 0
A maximum, minimum, or critical point
If f(x)= x2-4, and g is a differentiable function of x, what is the derivative of f(g(x))
2g'(x)
What is the integral of du/u
ln|x|+C
What is the product rule
fg'+gf'
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
Find d/dx (fgh)
(fg)dh/dx+(fh)dg/dx+(gh)df/dx
What does this stand for T.F.T.O.C?
The Fundamental Theorem of Calculus
What is the derivative of the natural log of x?
1/x
Derivative of cot x
-csc2x
How do you decided if a point is a point of inflection
If the concavity changes from negative to positive or positive to negative
Find the derivative of f(x)=(lnx)/(x)
f'(x)= (1-ln x)/(x^2)
Step 1: Set up the Primary Equation
Step 2: Set up the Secondary Equation
Step 3: Find the Absolute Max or Min
What I am trying to find?
The Optimization
Write the chain rule?
f'(g(x)) times g'(x)
Derivative of sec x
sec x tan x
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
F(x)= 2x3-3x2-12x+18, when is the graph decreasing and concave up?
(-1, .5)
Solve this problem by using integration: [-1,1]; f(x)=1/x2
Can't be solve because the function is undefined on the interval.