derivative definitions

1D-

if f’(x) is POSITIVE on an interval, then f(x) is _____ on that interval

1D-

if f’(x) is POSITIVE on an interval, then f(x) is _____ on that interval

INCREASING

1D-

if f’(x) is NEGATIVE on an interval, then f(x) is _____ on that interval

DECREASING

1D-

if f’(x) changes from POSITIVE TO NEGATIVE at x=c, then x=c is a relative ________ for f(x)

MAXIMUM

1D-

if f’(x) changes from POSITIVE TO NEGATIVE at x=c, then x=c is a relative ________ for f(x)

MAXIMUM

1D-

if f’(x) DOES NOT CHANGE SIGNS at a critcal number then their is ____________ at a that critcal number

NEITHER A RELATIVE MAXIMUM OR RELATIVE MINIMUM

2D-

If f”(x)>0 on interval (a,b), then the graph of f(x) is ___________ on interval (a,b)

CONCAVE UP

2D-

If f”(x)<0 on interval (a,b), then the graph of f(x) is ___________ on interval (a,b)

CONCAVE DOWN

2D-

when the 2nd Derivative CHANGES SIGNS at x=c, then x=c is called a __________________

POINT OF INFLECTION

2D-

If the graph of f(x) lies ABOVE its tangent lines on interval I, then the graph is _________ on interval I

CONCAVE UP

2D-

If the graph of f(x) lies BELOW its tangent lines on interval I, then the graph is _________ on interval I

CONCAVE DOWN

2D-

When the first derivative is INCREASING then the second derivative is ___________ and f(x) is _____________

POSITIVE, CONCAVE UP

2D-

When the first derivative is DECREASING then the second derivative is ___________ and f(x) is _____________

NEGATIVE, CONCAVE DOWN

2D-

When the first derivative CHANGES from INCREASING to DECREASING or VICE VERSA then at x=c, then x=c is a ___________

POINT OF INFLECTION

2D Test-

If f’(c)=0 and f”(c)>0 then x=c is a local _________

MINIMUM

2D Test-

If f’(c)=0 and f”(c)<0 then x=c is a local _________

MAXIMUM