onegirl
Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0



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onegirl
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@satellite73 can u help please?

anonymous
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this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"

anonymous
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take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula

anonymous
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since the point is \((0,0)\) the equation of the line will be \(y=3x\)

onegirl
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ok so find the derivative of sin 3x right?

anonymous
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yes

onegirl
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Ok so i got 3cos(3x)

anonymous
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yes
now evaluate at \(x=0\) to find your slope

onegirl
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ok i got 3

anonymous
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yes

anonymous
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that is the slope of your line

onegirl
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okay so now i have to use the point slop formula?

anonymous
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yes

anonymous
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but the point is \((0,0)\) so it is just \(y=3x\)

onegirl
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okay so what do i do next?

anonymous
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you are done

onegirl
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okay

electrokid
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linear approximation of f(x) at x=x0:
\[f(x)=f(x_0)+(xx_0)f'(x_0)\]

electrokid
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you can use this way too. (notice the resemblance to equation of line)