AP Calculus Chapter 3
Card Set Information
AP Calculus Chapter 3
AP Calculus BC Chapter
These are my flashcards for the third chapter of my book, Calculus of a single variable AP edition
Values of x in the domain of f (x) where f 'x= 0 or f 'x is undefined
How do you find absolute minimums and maximums on a closed interval?
1. Find critical numbers
2. Find values for the function at each endpoint and critical number
3. Determine absolute max and absolute min for the interval by your results from step 2.
If f is differentiable on the interval (a , b) and f(a) = f(b) then there is at least one place in the interval
where f 'x= 0
Mean Value Theorem (MVT)
If f (x) is continuous and differentiable on the interval [a , b], there is someplace in the interval where f ' x
equals the slope of the line going through the endpoints of the interval.
First Derivative ITSC
1) Use critical numbers to determine intervals.
Sign of f ' x
If sign of f ' x is positive what is happening to f(x)?
f(x) is increasing
If sign of f ' x is negative then f(x) is _______.
f(x) is decreasing
First Derivative Test
Do a first derivative ITSC,
If f ' x is changing from pos to neg, then relative max
If f ' x is changing from neg to pos, then relative min
f'(x) is increasing, f''(x)is positive, f(x) will hold water
f ' x is decreasing, f '' x is negative, f (x) will shed water
Second Derivative ITSC
Find where the 2nd Derivative is 0 or undefined. Use those numbers to make intervals
Sign of f '' x
If f '' x is positive
interval is concave up
If f '' x is negative,
interval is concave down
Where the function is switching from concave up to concave down or
from concave down to concave up.
2nd Derivative Test
1. Plug your critical numbers into the 2nd Derivative
2. If the result is positive, then the there is a relative min at the critical
3. If the result is negative, then there is a relative max at the critical
4. If the result is 0, the test fails
Definition of a Differential
Definition of Δy
Δy= f(x+Δx) − f(x)
1. Write your two equations. The equation that you are minimizing or maximizing is the Primary Equation.
2. Get your Primary equation in terms of one variable by substituting in the other equation.
3. Differentiate your primary equation and find the critical numbers.
4. Show that the critical numbers are a max or min by the 2nd Derivative Test or a First Derivative ITSC
5. Answer the question.