Midterm Flashcards
Def. Of continuity
A function is continuous at a value, c, if:
- f(c) is defined
- lim f(x) as ‘x approaches c’ exists
- f(c) = lim f(x) as ‘x approaches c’
Critical numbers theorem
A critical number is a value c such that f’(c)= 0 or f’(c) is undefined
Extreme value theorem
If you look at a function on a closed interval na absolute maximum or an absolute minimum exists
Rolle’s theorem
Let f be a function that is continuous on [a, b], differentiable on (a, b), and f(a) = f(b). Then there is at least one value c in (a, b) such that f’(c)= 0
Mean value theorem
Let f be a function that is continuous on [a, b] and differentiable on (a, b). Then there is at least on number c in (a, b) such that f(c)= [f(b)-f(a)]/[b-a]
If the derivative is _______, the the function is increasing
Positive
If the derivative changes from __(1)__ to ___(2)__ at x= c, then x=c is a local minimum
- Negative
1. Positive
When velocity and acceleration of the particle have different signs, the particle is _____.
Slowing down
The derivative of position is ______
Velocity
The derivative of a velocity function is _______
Acceleration
If the derivative is _______, then the function is decreasing
Negative
If f’‘(x) > 0 on Interval I, then the graph of f(x) is a _________ on Interval I
Concave up
If graph of f(x) lies ________, on Interval I, then the graph is concave up on Interval I
Above it’s tangent line
If _____ on Interval I, then the graph of f(x) is concave down
f’‘(x)<0
If graph f(x) lies below it’s tangent line on Interval I, then the graph is _____ on Interval I
Concave down
