Lena772
  • Lena772
(a) find an equation of the tangent line to the graph of at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Lena772
  • Lena772
function: y= cos 3x point: (pi/4, -sqrt2/2)
ganeshie8
  • ganeshie8
where wer u stuck ?
ganeshie8
  • ganeshie8
i saw u doing a similar problem the other day ? :)

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anonymous
  • anonymous
take the derivative
Lena772
  • Lena772
I just get confused when trig is added in
anonymous
  • anonymous
do you know what the derivative is
Lena772
  • Lena772
dy/dx
anonymous
  • anonymous
-3sin3x
anonymous
  • anonymous
right
Lena772
  • Lena772
yes
ganeshie8
  • ganeshie8
so, slope = m = dy/dx = -3sin3x
ganeshie8
  • ganeshie8
since u want the slope at point: (pi/4, -sqrt2/2) evaluate slope at x = pi/4
ganeshie8
  • ganeshie8
dy/dx at x = pi/4 :- -3sin(3*pi/4) = ?
Lena772
  • Lena772
-0.123
Lena772
  • Lena772
@ganeshie8
ganeshie8
  • ganeshie8
that doesnt look right you should get :- dy/dx at x = pi/4 :- -3sin(3*pi/4) = \(\large \frac{-3}{\sqrt{2}}\)
ganeshie8
  • ganeshie8
now that u knw slope, m = \(\large \frac{-3}{\sqrt{2}}\) point: (pi/4, -sqrt2/2) wats the equation of tangent in point slope form ?
Lena772
  • Lena772
y-(-sqrt2/3)=(-3/sqrt2)(x-(pi/4)
Lena772
  • Lena772
?
Lena772
  • Lena772
@hartnn
ganeshie8
  • ganeshie8
thats right !
Lena772
  • Lena772
So that's for a? What would the graph look like for b? Do I just put that equation into Geogebra?
Lena772
  • Lena772
@ganeshie8
ganeshie8
  • ganeshie8
yup graph all 3 below :- 1) function: y= cos 3x 2) point: (pi/4, -sqrt2/2) 3) tangent : y-(-sqrt2/\(\color{red}{2}\))=(-3/sqrt2)(x-(pi/4)
ganeshie8
  • ganeshie8
u should get exactly like the one attached
1 Attachment

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