onegirl
Find an equation of the tangent line y = f(x) at x = a. f(x) = sin 4x, a = pi/8
Delete
Share
This Question is Closed
zepdrix
Best Response
You'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 slope-intercept form: \(\large y=mx+b\),
Or in point-slope form: \(\large y-y_o=m(x-x_o)\).
onegirl
Best Response
You've already chosen the best response.
0
in slope intercept from
zepdrix
Best Response
You'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.
onegirl
Best Response
You've already chosen the best response.
0
okay hold on
onegirl
Best Response
You've already chosen the best response.
0
when i find the derivative a = pi/8 is not int he equation right?
onegirl
Best Response
You've already chosen the best response.
0
the*
onegirl
Best Response
You've already chosen the best response.
0
i got sin(4)
zepdrix
Best Response
You'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.
onegirl
Best Response
You've already chosen the best response.
0
okay
onegirl
Best Response
You've already chosen the best response.
0
i got 4 cos(4x)
zepdrix
Best Response
You've already chosen the best response.
1
ok good, now plug in x=pi/8 :D
onegirl
Best Response
You've already chosen the best response.
0
ok
onegirl
Best Response
You've already chosen the best response.
0
i got 0 after i plugged in and solved
zepdrix
Best Response
You'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.
zepdrix
Best Response
You'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.
onegirl
Best Response
You've already chosen the best response.
0
ok
onegirl
Best Response
You've already chosen the best response.
0
so i should plug in pi/8 into y = mx + b?
zepdrix
Best Response
You've already chosen the best response.
1
no, plug it into your original function, before you took the derivative of it.
onegirl
Best Response
You've already chosen the best response.
0
ohh okay
onegirl
Best Response
You've already chosen the best response.
0
so sin 4(pi/8) ?
onegirl
Best Response
You've already chosen the best response.
0
okay so i got 1
zepdrix
Best Response
You'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 \(\large b\).
onegirl
Best Response
You've already chosen the best response.
0
ok so y = 0x + b so i should plug it in place of b?
zepdrix
Best Response
You've already chosen the best response.
1
No, your coordinate pair is \(\large (x,\;y)\). Plug it into those.
onegirl
Best Response
You've already chosen the best response.
0
ohh ok got it
onegirl
Best Response
You've already chosen the best response.
0
okay so 1 = 0(pi/8) + b
zepdrix
Best Response
You've already chosen the best response.
1
So what is your b value? :3
onegirl
Best Response
You've already chosen the best response.
0
Lol sorry i got 1 :)
onegirl
Best Response
You've already chosen the best response.
0
b = 1
zepdrix
Best Response
You'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,\[\large y=1\]
onegirl
Best Response
You've already chosen the best response.
0
okay
zepdrix
Best Response
You'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.
zepdrix
Best Response
You've already chosen the best response.
1
It's not too difficult, just a lot of silly letters :) Keep practicing!
onegirl
Best Response
You've already chosen the best response.
0
okay so our equation is complete? and yes just lot to do and thanks
zepdrix
Best Response
You've already chosen the best response.
1
Yes, that's our final answer.