Limits
limx→3(2x+1)
7
f(x)=x3+4x2
3x2+8x
A derivative tells the _____ of a function.
rate of change
∫xdx
x2/2 + c
The value a function approaches as x approaches a certain number.
Limit
limx→1(x2+5x)
6
Find:
d/dx (3x2+2x-7)
6x+2
If f′(x) > 0, the function is _____.
increasing
∫4x3dx
x4+c
The instantaneous rate of change of a function.
Derivative
limx→0 sin(x)/x
1
d/dx (x2sin x)
2xsin(x)+x2cos(x)
If f′′(x) < 0, the graph is _____.
concave down
∫ xdx
Find the integral from 0 to 2
2
The area under a curve represented mathematically.
Integral
limx→4 x2-16/x-4
8
d/dx (x1/2)
1/ (2 x1/2)
At a local max, f′(x) equals _____.
0
The derivative of an integral is explained by the _____.
Fundamental Theorem of Calculus
A line that touches a curve at exactly one point and has the same slope there.
Tangent line
Determine if continuous at x = 2:
f(x)={x+1,x<25,x=2x2,x>2f(x)=⎩⎨⎧x+1,5,x2,x<2x=2x>2
No
d/dx (ex+x3)
ex+3x2
A particle’s position is s(t). The derivative s′(t) is _____.
velocity
∫cosxdx
sin(x) + C
A point where the derivative is zero or undefined, often indicating a max/min.
Critical point