Is this right?

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

I used the linearization equation y=f (a) + f' (a) (x-a)

y=f (3pi/4) + f' (3pi/4) (x-3pi/4)

y=tan (3pi/4) + sec^2 (3pi/4) (x-3pi/4)

y = - 1+2 (x-3pi/4)

y = - 1+2x-3pi/2

2y=4x-3pi-2

Is this correct?

Question

Mathematics

Marcel Fisher

10 June, 18:24

Is this right?

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

I used the linearization equation y=f (a) + f' (a) (x-a)

y=f (3pi/4) + f' (3pi/4) (x-3pi/4)

y=tan (3pi/4) + sec^2 (3pi/4) (x-3pi/4)

y = - 1+2 (x-3pi/4)

y = - 1+2x-3pi/2

2y=4x-3pi-2

Is this correct?

+5

Answers (1)

Know the Answer?

Rocco Merritt · Answer 1

Yes you have the correct steps and answer. Nice job.

Optionally, you can solve for y to get

2y = 4x-3pi-2

y = (4x-3pi-2) / 2

y = 2x-1 - (3pi/2)

which is another way to express the equation you got. There are many ways to write the answer.

Is this right?Which of the following is the best linear approximation for f (x) = tan (x) near x = 3pi/4?I used the linearization equation y=f (a) + f' (a) (x-a)y=f (3pi/4) + f' (3pi/4) (x-3pi/4)y=tan (3pi/4) + sec^2 (3pi/4) (x-3pi/4)y = - 1+2 (x-3pi/4)y = - 1+2x-3pi/22y=4x-3pi-2Is this correct?