MathTV Topic - The First Derivative and the Behavior of Functions

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Applying the Derivative
The First Derivative and the Behavior of Functions

Problem 1

Discuss the behavior of \(N(t)\) in terms of increasing and decreasing.

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Mr. Damarest

Molly S.

Octabio

Problem 2

Find the interval on which \(f(x)=x^2-4x\) is increasing and the interval upon which it is decreasing.

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Molly S.

Octabio

Problem 3

Discuss the first derivative and its relationship to the graph of \(g(x)=4\).

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Molly S.

Octabio

Problem 4

Find the relative extrema for \(f(x)=x^4-8x^2\)

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Mr. Damarest

Molly S.

Octabio

Problem 5

Construct a sign chart for the graph shown in Figure 16 and use it to construct a summary table for the function.

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Octabio

Molly S.

Octabio

Problem 6

Assuming the model \(C(t)=\dfrac{7}{5t^2+20}\) to be true, should the manufacturerâ€™s claims be accepted or rejected?

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Joshua

Molly S.

Octabio

Problem 7

Find, if they exist, the absolute maximum and minimum of the function \[f(x)-(x-4)^\frac{2}{7}+3\] on the interval \([0,6]\).

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Mr. Damarest

Octabio

Lauren

Octabio

Problem 8

Find, if they exist, all relative and absolute extrema of the function \[f(x)=\frac{1}{x-4}\]

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Mr. Damarest

Octabio

Lauren

Octabio

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