Derivatives
y=4x3 + 7x2+ 2x + 3
y1=12x2 + 14x + 2
What is the definition of Calculus?
The study of rates of change
What is Leibniz's notation?
dy/dx
Lim x→2-
1/x2 -4
-∞
y=√1+2x+2x
y1= 4
What is the definition of a secant line?
The average rate of change (slope)
What is Lagrange's notation?
f1(x)
Lim x→2+
3/x-2
∞
y=x2+3x+5
y1=2x+3
What is the definition of a tangent line?
The instantaneous rate of change (derivative)
Y = 12x5 + 3x4+ 7x3 + x2 − 9x + 6 Find d4y/dx4
fIIII(x)=1440x + 72
Lim x→-1
x+1/x2-1
-1/2
y= -1/4x+1
y1=-1/4
What is the definition of a difference quotient?
The measure of the average rate of change of the function over an interval
y=4x4+3x3+5x2 Find d4y/dx4
fIIII(x)= 96
Lim x→3+
-x2/3x-9
-∞
y=cos(2x+3)
y1=-2sin(2x+3)
What are the four concepts of Calculus?
1. Limits
2. Differentiation
3. Integration
4 Function Theory
y=2x5+2x3+3x2 Find d4y/dx4
fIIII(x)=240x
Lim x→ -π/3
sec(x)
2