Limits
Derivatives
Tangents and Normals
Sign Diagrams
Graphs
100
lim_(x->3)2x
What is 6?
100
The derivative of
3x^2+5x
What is
6x+5
100
The gradient of the tangent of f(x)=x^2-4x+5 at x=-6
What is -16?
100
The classification of any stationary points of f(x) given the sign diagram.
What is
a local maximum at
x=8
100
The interval(s) on which f(x) graphed below is decreasing.
What is
x<0
1.75<=x<=2
200
lim_(x->0)4+x
What is 4?
200
f'(x) given
f(x)=4x^5-7x^3+5x-6
What is
20x^4-21x^2+5
200
The equation of the tangent of
f(x)=x^2-4x+5 at x=-6
What is
y=-16x-31
200
The classification of any stationary points of f(x) given the sign diagram.
What is
a local min at x=2
a stationary inflection point at x=3
a local max at x=4
200
The points at which f'(x)=0 given f(x) graphed below.
What are (0,0), (1.75,4.02), and (2,4)?
300
lim_(x->oo)f(x)
graphed below.
What is 0?
300
dy/dx given
y=2/3x^6+1/2x^5
What is
4x^5+5/2x^4
300
The equation of the normal of
f(x)=x^2-4x+5 at x=-6
What is
y=1/16x+65.375
300
The sign diagram for f'(x) given
f(x)=x^2-6x+8
What is 
300
The local min of f(x) given f(x) graphed below on the interval
-0.5 ≤ x ≤ 0.4
What is (0,.09)?
400
lim_(x->2)f(x)
graphed below.
What is 3?
400
f'(1) given
f(x)=1/x^2+6/x
What is -8?
400
The point at which the normal to f(x)=x^2-4x+5 at x=-6 crosses the curve again.
What is
(10.1,66.0)
400
The sign diagram for f'(x) given
f(x)=1/3x^3-5/2x^2+4x-1
What is
400
The global max of f(x) given f(x) graphed below.
What is (.4,1.233)?
500
lim_(h->0)(5xh-h^2)/h
What is
5x
500
f'(-2) given
f(x)=(3x^2-17x+4)/x
What is 2?
500
The y-intercept of the tangent to
y=3x^3-10x^2-4x-3 at
x=4
What is -227?
500
The interval(s) on which f(x) is increasing given that f'(x)=(3x-1)(x+4)(x-6)
What is
-4<=x<=1/3
x>=6
500
Interval(s) on which f'(x)<0 given f(x) graphed below.
What is -.536 ≤ x ≤ 0?