Question

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

Answer 1

HI!

Answer 2

do you know the derivative of tangent?

Answer 3

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

Answer 4

then use the point slope formula

Answer 5

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

Answer 6

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

@misty1212

Answer 7

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

Answer 8

how do i do that?

Answer 9

@misty1212

Answer 10

multiply out on the right then multiply all by 2

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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