Question

Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sqrt(x), x o = 1

Answer 1

@zepdrix can u help?

Answer 2

linear approx is:
\[y=f'(c)(x-c)+f(c)\]

Answer 3

i tried but i got stuck is this correct so far?

L(x) = f(1) + f'(1) (x - 1)
= 0 + 1/2sqrt(x) ( x - 1)

Answer 4

f(1) = 1, not 0

f'(1) = 1/2

Answer 5

therefore: the linear approximation if say: sqrt(1.2) is\[y=1+\frac12(1.2-1)=1.1\]

Answer 6

umm so i made a mistake on the 0 right?

Answer 7

yep, and also on the f'(1)

f'(1) not equal 1/2sqrt(x)

Answer 8

ohh okay

Answer 9

f'(1) = 1/2sqrt(1) = 1/2

Answer 10

so its 1 + 0 ( x - 1) ?

Answer 11

??? is it correct?

Answer 12

no, 0 does not equal 1/2

Answer 13

\[y=f(1)+f'(1)(x-1)\]
\[y=1+\frac12(x-1)\]

Answer 14

ohh ok