5.1 Using MVT

AP calculus, unit 5, main ideas/ takeaways

Recap of IVT. Describe what it is.

A function y = f(x) that’s continuous on a closed intervals [a,b] takes every value.

What does MVT mean?

main value theorem

Describe MVT

There’s a point where the AROC = IROC over the given interval on a continuous and differentiable function.

AROC in full?

average rate of change

IROC in full? another word for it?

Instantaneous rate of change AKA derivative

First step when finding whether MVT applies

Use the intervals given to find the AROC

Second step when finding whether MVT applies

Find the derivative, if it’s not already given

third and last step when finding whether MVT applies

make AROC = IROC

Things to double check for

Continuity and differentiability

What does it mean for a graph to be continous?

no holes/ you can draw the graph without picking up your writing utensil.

what does it mean for a graph to be defferentiable?

No cusps or corners

What does it mean when a graph is twice-differentiable?

Both the function and it’s derivative are continous.