how to find tangent line at a given point, without equation

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Find the equation of the line that is tangent to the curve at the point $(0,\sqrt{\frac{\pi}{2}})$. Given your answer in slope-intercept form.

I don't know how can I get the tangent line, without a given equation!!, this is part of cal1 classes.

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2 Answers

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If we suppose that your curve is the graph of a function $y=f(x)$ such that $f(0) = \sqrt{\pi/2}$, than the equation of the tangent at $x=0$ is:

$ y-\sqrt{\pi/2}=f'(0)(x-0) $

i.e.

$y=f'(0) x+\sqrt{\pi/2}$

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So far we can infer $$ T(x) = m x + n $$ with $T(0) = \sqrt{\pi/2}$. Thus $$ T(x) = m x + \sqrt{\pi/2} $$ To determine the slope $m$ we need more information about the given curve.

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