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Problem 632

Graph the function \(\mathrm{y}=\mathrm{x}^{3}-9 \mathrm{x}\).

Expert verified

In summary:
- x-intercepts: \(-3, 0, 3\)
- y-intercept: \(0\)
- critical points: \(-\sqrt{3}, \sqrt{3}\)
- end behavior: \(y \rightarrow -\infty\) as \(x \rightarrow -\infty\) and \(y \rightarrow +\infty\) as \(x \rightarrow +\infty\)
With these features, sketch the graph of the function \(y = x^3 - 9x\).

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Chapter 21

Locate the roots of \(^{3}-3 \mathrm{x}^{2}-6 \mathrm{x}+9=0\)

Chapter 21

Determine the real values of \(\mathrm{x}\) for which $\sqrt{\mathrm{x}}^{3}-3 \mathrm{x}^{2}+2 \mathrm{x}$ is real.

Chapter 21

Show that \(\mathrm{x}^{3}>\mathrm{y}^{3}\) if \(\mathrm{x}>\mathrm{y}\)

Chapter 21

Solve \(x^{4}+y^{4}=82\) (1), \(x-y=2\)

Chapter 21

If \(\mathrm{a} / \mathrm{b}=\mathrm{c} / \mathrm{d}=\mathrm{e} / \mathrm{f}\), show that $\left(a^{3} b+2 c^{2} e-3 a e^{2} f\right) /\left(b^{4}+2 d^{2} f-3 d f^{3}\right)=a c e / b d f$

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