Question

Find the linearization L(x) of the function at a = 8.
f(x) = x^(2/3)...
I got it to be (8/3)x-(4/3)...and its wrong....

Answer 1

f(a)-df(a)(x-a)

Answer 2

....still confuse

Answer 3

f(a) = a^(2/3) = 8^(2/3) = 4
df(x) = (2/3)x^(-1/3)
df(a) = 2/3 * 8 ^(-1/3) = 1/3
x-a = x-8
so f(x) = 4-(1/3)(x-8)
f(x) = 4 - (x-8)/3 = -x/3 +20/3

Answer 4

all you are doing is finding the tangent line of f(x) at a=8

Answer 5

i had 4/3x-20/3

Answer 6

dhatraditya.....the second part is wrong its df(x)=(2/3)x^(1/3) not -1/3

Answer 7

(8,8^(2/3))=(8,4) is point on the tangent line
we can find the slope by finding f'(x) and evaluate f' at x=8
f'(x)=2/3*x^(-1/3)
f'(8)=2/3*(8)^(-1/3)=1/3
tangent line has form y=mx+b
we know a point and we know the slope so we can find the y-intercept
4=1/3*(8)+b
4-8/3=b
4/3=b
so the tangent line is y=1/3*x+4/3

Answer 8

2/3 -1 = -1/3

Answer 9

rmalik, do you understand?

Answer 10

kinda....

Answer 11

L(x)=1/3*x+4/3 is the linearization at a=8 of f(x)=x^(2/3)

Answer 12

all you have to do is find the equation of the tangent line