Question

Find the linear approximation to f(x) = sqrt{25-x ^{2}} near 3.

Answer 1

Linear approximation just means find the tangent line to f at x=3

Answer 2

so all I need to do is find f'(3)?

Answer 3

well that is the slope of the tangent line

Answer 4

you need to find the tangent line

Answer 5

oops, that's what I meant.

Answer 6

y=f'(3)(x-3)+f(3)

Answer 7

so for f'(3) I got 3/16, but what do I plug in for x in (x-3)?

Answer 8

i mean 3/4, not 3/16.

Answer 9

do you mean -3/4?

Answer 10

oh my goodness. yes. finals are killing me, can you tell?

Answer 11

so we have y=-3/4 *(x-3)+f(3)

Answer 12

all you have to do now is find f(3)

Answer 13

this is your linear approximation for values near x=3

Answer 14

and I'm talking about y=-3/4 * (x-3)+f(3)

Answer 15

okay, so x-3 will just stay in my answer?

Answer 16

all i was doing was using the point slope formula to find the tangent line
y-y_1=m(x-x_1)
I just added y_1 on both sides
y=m(x-x_1)+y_1

x_1 is 3
y_2 is f(3)

Answer 17

if you want to distribute the -3/4 and combine like terms you may want to if you are entering answers into a machine