Professor Curious | Talk to an AI Tutor That Explains Until It Clicks

Explain the concept of average rate of change.

Measures how much a function's output changes over a specific interval; the slope of the secant line.

Flip to see [answer/question]

Revise later

SpaceTo flip

If confident

All Flashcards

Explain the concept of average rate of change.

Measures how much a function's output changes over a specific interval; the slope of the secant line.

What does a positive rate of change indicate?

That the function is increasing as the input increases.

What does a negative rate of change indicate?

That the function is decreasing as the input increases.

What is the formula for average rate of change over the interval [a, b]?

$\frac{f(b) - f(a)}{b - a}$

How do you calculate the average rate of change of $f(x)$ over $[a, b]$ ?

Find $f(a)$ and $f(b)$ . 2. Calculate $f(b) - f(a)$ . 3. Calculate $b - a$ . 4. Divide $(f(b) - f(a))$ by $(b - a)$ .

How do you determine if a function is increasing or decreasing?

Calculate the rate of change. 2. If the rate is positive, the function is increasing. 3. If the rate is negative, the function is decreasing.