Which of the following is the best linear approximation for f(x) = tan(x) near x equals 3 times pi divided by 4?

Question

misty1212 · Answer

HI!

misty1212 · Answer

do you know the derivative of tangent?

misty1212 · Answer

the slope will be 
$$\sec^2(\frac{3\pi}{4})$$

misty1212 · Answer

then use the point slope formula

misty1212 · Answer

the point will be $$(\frac{3\pi}{4},-1)$$

anonymous · Answer

It gives me options of 
2y=4x-3pi-2
2y=2x-3pi-1
2y=4x-3pi-1
2y=x-3pi-2

@misty1212

misty1212 · Answer

$$\sec^2(\frac{3\pi}{4})=2$$so you can start with 
$$y+1=2(x-\frac{3\pi}{4})$$ and try to change to "standard form"

anonymous · Answer

how do i do that?

anonymous · Answer

@misty1212

misty1212 · Answer

multiply out on the right then multiply all by 2

misty1212 · Answer

$$y+1=2(x-\frac{3\pi}{4})\
y+1=2x-\frac{3\pi}{2}\
2y+2=4x-3\pi$$

misty1212 · Answer

looks like it will be choice A
$$2y+4x-3\pi-2$$

anonymous · Answer

Okay I had the second line, but then I got confused from there.  Thank you!

misty1212 · Answer

$\color\magenta\heartsuit$$\color\magenta\heartsuit$