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

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

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

Assuming the model \(C(t)=\dfrac{7}{5t^2+20}\) to be true, should the manufacturer’s claims be accepted or rejected?

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

Describe the behavior of the function \[f(t)=-t^3+9t^2 \qquad 0\leq t\leq 8\] in the context of this problem.

Describe the behavior of the function \[f(x)=x^\frac{3}{5}-1\]

Summarize the behavior of \(f(x)=x^3-3x^2+4\) and sketch its graph.

Summarize the behavior of \(f(x)=\dfrac{5x+2}{3x-4}\) and sketch its graph.

Assuming the function \(R(x)=-\dfrac{1}{4}x^4+200x^2\) is true, should the website’s managers accept or reject this forecast?

Use the second derivative test to find all the relative extrema of the function \[f(x)=x^3+\frac{9}{2}x^2-12x+11\]

The revenue realized by a company on the sale of \(x\) units of its product is given by the revenue function \[R(x)=x^3+4x^2+160x\] Compute and interpret both \(R(70)\) and \(R'(70)\).

The cost to a company to produce \(x\) units of a product is given by the cost function \[C(x)=-0.035x^2+40x+25\] Compute and interpret both \(C(600)\) and \(C'(600)\).