Unit 4 apcalc

What to write in proving mvt

1. F is continuous on [,] and differentiable in all values of (,)

2. Do average rate of change

3. The mvt tells us that there is an x value in (,) such that f(x)= that number.

What is required for mvt to work

• the function f must be differentiable at the open intervals

• Function f must be continuous at open intervals

What is required for relative extrema

• the x value of extrema must be continuous for the parent function and differentiable for the derivative function of the parent function

Writing inc/dec

F’ is pos/neg at for x in intervals…therefore, F is inc/dec at …

Writing relative min. and max.

F’ is changing from neg to pos at x=…, (f is continous on x=) so f has a relative min at that x value

Dont forget to label the type of function used for numberline

M

When finding the paired coordinates for the max and min both rel and abs…

Plug the x value into the parent function

How to know if it is asking you for mvt or ivt

Mvt needs both parent and deriv reference

Ivt has nothing to do with deriv, just needs continuity

Mvt uses what type of brackets where?

Uses open brackets for showinf differentiability

Rolles theorem

When mvt comparing two slopes that are zero

Critical numbers include what type of numbers?

Both undefined and those that make the function zero

Do you need to care about undiff critical numbers in ABS extrema?

No

quotient rule

If given a graph and told to find where the relative extrema or where the function is decreasing/increasing, look at the y values of the graph and find where they transition from positive to negative, when looking for where the line is under the y axis, the critical points qre where its (0,0), note the intervals with open brackets, its still a open interval if the critical number is a hole