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Find an equation of the tangent line y = f(x) at x = a. f(x) = sin 4x, a = pi/8
 one year ago
 one year ago
Find an equation of the tangent line y = f(x) at x = a. f(x) = sin 4x, a = pi/8
 one year ago
 one year ago

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zepdrixBest ResponseYou've already chosen the best response.1
Hmm I think you've done a few of these types of problems. So I'm just curious, which result makes more sense to you. Seeing our tangent line in slopeintercept form: \(\large y=mx+b\), Or in pointslope form: \(\large yy_o=m(xx_o)\).
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
in slope intercept from
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Ok we will have 2 pieces we need to find. \(\large m\) is the slope of our tangent line. Take the derivative of your function, and evaluate it at \(\large x=\pi/8\). That will be your \(\large m\) value.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
when i find the derivative a = pi/8 is not int he equation right?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Take the derivative of sin(4x) first. Don't plug a=pi/8 in until after you've taken a derivative.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
ok good, now plug in x=pi/8 :D
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
i got 0 after i plugged in and solved
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Ok sounds good. So we've determined that the slope \(\large m\) of our tangent line will be 0. \[\large y=mx+b \qquad \rightarrow \qquad y=0x+b\] Now we just need to find the \(\large b\) value.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
To find it, we'll need to plug in a coordinate pair that falls on the line. Well, since our line is tangent to the curve at x=pi/8, we can plug x=pi/8 into that function to get a corresponding y value. This will be the coordinate pair we'll plug into our tangent line.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so i should plug in pi/8 into y = mx + b?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
no, plug it into your original function, before you took the derivative of it.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So that gives us a coordinate pair of \(\large \left(\dfrac{\pi}{8},\;1\right)\). Plug that into your tangent function to solve for \(\large b\).
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
ok so y = 0x + b so i should plug it in place of b?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
No, your coordinate pair is \(\large (x,\;y)\). Plug it into those.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay so 1 = 0(pi/8) + b
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So what is your b value? :3
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Ok sounds good. So if we plug that missing \(\large b\) into our tangent line equation, we get,\[\large y=0x+1\]Which can be simplified to,\[\large y=1\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
I guess it's really 3 steps. We had to find ~\(\large m\) ~\(\large b\) ~A Coordinate Pair.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
It's not too difficult, just a lot of silly letters :) Keep practicing!
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay so our equation is complete? and yes just lot to do and thanks
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yes, that's our final answer.
 one year ago
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