Question

find linearization of (64+3x^2)^(-1/2)

Answer 1

this means find the equation of the line tangent to the curve
but to do this you need a point as well

Answer 2

at a=0 that would be the point right?

Answer 3

i plug zero into the derivative to get the slope?

Answer 4

i don't know, you cannot assume the point is a = 0 you must be told

Answer 5

you can only find the linearization at a point, so you have to be told both the function and a point

Answer 6

that is the point i was given i just forgot to write it

Answer 7

would this be correct.. y=1/8+512(x-0)?

Answer 8

oh ok
find the derivative, replace x by 0 and get the slope, then use point slope formula
lets see what we get

Answer 9

\[f(x)=(64+3x^2)^{-1/2}\]
\[f'(x)=-\frac{3x}{(64+3x^2)^{\frac{3}{2}}}\]

Answer 10

hmm i get
\[f'(0)=0\] did i make a mistake?

Answer 11

oh no i got zero too

Answer 12

so plug that into point slope formula is that what i do?