Question

Linearize f(x)=10x^2-5x+2 Near: a. x0 =8, x0 = 5. Find:a. y:b. y:

Answer 1

OK so you know the formula for linear approximation?

Answer 2

L(x)f'(a)(x-a)+f(a)?

Answer 3

ok.
looks fine. but you take a as x0. as given in your question. i.e.\[f(x)\approx f(x_0)+f'(x_0)(x-x_0)\]Ist it clear to you?

Answer 4

@nycsmilez

Answer 5

I did that and got the wrong answer
I have to find the dervative of the eqution and plug in the 8 into the dervative and then from there do the formular?

Answer 6

Why did you get wrong answer. let us try here. So yo have two conditions.
\[\text{a) }x_0=8\]and\[\text{b) }x_0=5\]Am I right nycsmilez?

Answer 7

Yes, so the Derviative for the eqution is 20x-5
from there i plug in the 8 = 20(8)-5 = 155
from there
L(x)= 155(x-8) + 602 which i got from pluging in the 8 into the orginal equation?

Answer 8

from there i got 155x-638 Is that the answer?

Answer 9

ok wait let me see.

Answer 10

yes yes . it is your answer.

Answer 11

When i put the answer it says im wrong

Answer 12

no. it is right. i am 100% sure.

Answer 13

ok thanx you

Answer 14

so y = 155x-638

Answer 15

\[L(x)\approx f(x_0)-f'(x_0)(x-x_0)-----(1)\]
f'(x)=20x-5 and f'(x0)=20(x0)-5
Now use you equation (1)\[10x^2-5x+2\approx 10(x_0)^2-5x_0+2-[20x_0-5](x-8)\]replace x0=8\[\approx 10(8^2)-5(8)+2-[20(8)-5](x-8)\]\[\approx 640-40+2-(160-5)(x-8)\]\[\approx 602-155(x-8)\]\[\approx 155x-638\]

Answer 16

Your answer is correct. Don't worry it is right. Just believe on yourself. Good luck. and welcome. :)