`y = 4arccos(x-1) , (1, 2pi)` Find an equation of the tangent line to the graph of the function at the given point

Wednesday, June 3, 2015

$\displaystyle{y}={4}{\arccos{{\left({x}-{1}\right)}}},{\left({1},{2}\pi\right)}$ Find an equation of the tangent line to the graph of the function at the given point

The equation of the tangent line has the form

$\displaystyle{\left({y}-{y}_{{0}}\right)}={\left({x}-{x}_{{0}}\right)}\cdot{y}'{\left({x}_{{0}}\right)}.$

Here $\displaystyle{x}_{{0}}={1}$ and $\displaystyle{y}_{{0}}={2}\pi.$ This point is really on the graph, because $\displaystyle{y}_{{0}}={2}\pi$ is really equal to $\displaystyle{4}{\arccos{{\left({x}_{{0}}-{1}\right)}}}={4}{\arccos{{\left({0}\right)}}}={4}\cdot\frac{\pi}{{2}}={2}\pi.$

The derivative is $\displaystyle{y}'{\left({x}\right)}=-\frac{{4}}{\sqrt{{{1}-{{\left({x}-{1}\right)}}^{{2}}}}}.$ At $\displaystyle{x}={1}$ it is equal to $\displaystyle-{4},$ and the equation of the tangent line is

$\displaystyle{y}-{2}\pi={\left({x}-{1}\right)}\cdot{\left(-{4}\right)},{\quad\text{or}\quad}{y}=-{4}{x}+{4}+{2}\pi.$

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Wednesday, June 3, 2015

$\displaystyle{y}={4}{\arccos{{\left({x}-{1}\right)}}},{\left({1},{2}\pi\right)}$ Find an equation of the tangent line to the graph of the function at the given point

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Wednesday, June 3, 2015

Find an equation of the tangent line to the graph of the function at the given point

No comments:

Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{y}={4}{\arccos{{\left({x}-{1}\right)}}},{\left({1},{2}\pi\right)}$ Find an equation of the tangent line to the graph of the function at the given point

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?