Question

Find the linear approximation of the function
g(x) =
(1 + x)^1/3
at a = 0.

Answer 1

did you mean
at x = 0?

Answer 2

but in short, is very simple
it's just asking for the equation of tangent line at x = 0, if it's "x", not "a"
the tangent line, is a LINE, thus its equation, is a LINEAR equation
so, it's pretty much just asking on
what is the equation of the tangent line to that graph, when x = 0
simple
get the first derivative of g(x), to get the slope
get g(0) to get the y-coordinate
and then, just plug them all in the point-slope form

y - g(0) = m(x-0)