IVT and Rate of Change Warm Up

Which of the following formulas is used to find the average rate of change?

• $\frac{f\left(b\right)-f\left(a\right)}{a-b}$

• $\frac{f\left(b\right)-f\left(a\right)}{b-a}$

• $\frac{b-a}{f\left(b\right)-f\left(a\right)}$

• $\frac{b-a}{f\left(a\right)-f\left(b\right)}$

How many points are needed to make a secant line?

• 0

• 1

• 2

• 3

How many points are needed to make a tangent line?

• 0

• 1

• 2

• 3

What does the tangent line represent?

• Average Rate of Change

• Instantaneous Rate of Change

• Nothing

• Intermediate Rate of Change

What does the secant line represent?

• Average Rate of Change

• Instantaneous Rate of Change

• Nothing

• Intermediate Rate of Change

What condition must be met to use the Intermediate Value Theorem? The function must be...

• Continuous

• Even

• Odd

• It always applies

Can the IVT be applied to the function  $f\left(x\right)=\frac{1}{x-3}$  on the interval {0 , 5}?

• Yes

• No

Can the IVT be applied to the function  $f\left(x\right)=\frac{1}{x-3}$  on the interval {4 , 5}?

• Yes

• No

Assuming that f(x) is continuous on [0 , 6] how many solutions to f(x) = -1 guaranteed to have?

• 0

• 1

• 2

• 3

• Can't Be Determined