When solving a Mean Value Theorem question, the hypothesis about $$f$$ that you must write is

Since $$f$$ is Continous and differentiable, the Mean Value Theorem can be applied

Since $$f$$ is Continous, the Mean Value Theorem can be applied

Since $$f$$ is increasing, the Mean Value Theorem can be applied

Since $$f$$ is differentiable, the Mean Value Theorem can be applied

When solving an Intermediate Value Theorem question, the hypothesis about $$f$$ that you must write is

Since $$f$$ is Continous, the Intermediate Value Theorem can be applied

Since $$f$$ is Continous and differentiable, the Intermediate Value Theorem can be applied

Since $$f$$ is increasing, the Intermediate Value Theorem can be applied

Since $$f$$ is differentiable, the Intermediate Value Theorem can be applied

When you see $$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$$ , you think

Identify $$f\left(x\right)$$ , then find $$f$$

When you see "Explain why there exists a c such that $$f\left(c\right)=L$$ , you think

IVT. Write "Since $$f\left(x\right)$$ is continuous, the IVT applies. Since...(lower), and ....(higher), there exists a c such that $$f\left(c\right)=L$$

Tangent line. $$y-y_1=m\left(x-x_1\right)$$

IVT. Write since...(lower) and ...(higher), there exists a c such that $$f\left(c\right)=L$$

To determine if a particle is speeding up or slowing down at time $$r$$ , the first thing you need to do is

Find $$v\left(r\right)$$ and $$a\left(r\right)$$

Compare the signs to determine if they are the same or opposite

Make a sign chart for $$v\left(t\right)$$

Make a sign chart for $$a\left(t\right)$$

Is there ever a time $$r$$ on the interval $$\left[0,5\right]$$ such that $$W\left(r\right)=15$$

Since $$W\left(t\right)$$ is continuous, the Intermediate Value Theorem can be applied. Since $$W\left(0\right)=10<15$$ and $$W\left(2\right)=20>15$$ , there must be an $$r$$ such that $$W\left(r\right)=15$$

Since $$W\left(t\right)$$ is continuous and differentiable, the Mean Value Theorem can be applied. $$\frac{W\left(5\right)-W\left(0\right)}{5-0}=\frac{30-10}{5}=\frac{20}{5}=4$$

Is there ever a time $$r$$ on the interval $$\left[0,5\right]$$ such that $$W$$

Since $$W\left(t\right)$$ is continuous and differentiable, the Mean Value Theorem can be applied. $$\frac{W\left(5\right)-W\left(0\right)}{5-0}=\frac{30-10}{5}=\frac{20}{5}=4$$

Since $$W\left(t\right)$$ is continuous, the Intermediate Value Theorem can be applied. Since $$W\left(0\right)=10<15$$ and $$W\left(2\right)=20>15$$ , there must be an $$r$$ such that $$W\left(r\right)=15$$

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CCSS

HSF.IF.B.4, 8.F.B.4, HSS.IC.B.4

Standards-aligned

William Stafford

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50 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When you see a question that says..
."Must there be a time..." or
"Is there a time r such that..."
you think this is either

Mean Value Theorem

Intermediate Value Theorem

Average Value

Average Rate of Change

Integral

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Factor and cancel

Compare limits to infinity

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When you see "Write the equation of the tangent line...", you think

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When you see "average rate of change", you think

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Rates, Tables, and Particle Motion

50 questions

When you see a question that says..
."Must there be a time..." or
"Is there a time r such that..."
you think this is either

When you see "Write the equation of the tangent line...", you think

When you see "average rate of change", you think

Find the distance the particle travels on [a,b]

Find the particle's displacement on [a,b]

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Rates, Tables, and Particle Motion

50 questions

When you see a question that says..."Must there be a time..." or"Is there a time r such that..."you think this is either

When you see "Write the equation of the tangent line...", you think

When you see "average rate of change", you think

Find the distance the particle travels on [a,b]

Find the particle's displacement on [a,b]

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

When you see a question that says..
."Must there be a time..." or
"Is there a time r such that..."
you think this is either