Question

Use linear approximation, i.e. the tangent line, to approximate (the 3 is inside the v part if you know what I mean, it's not 3 times sqrt) 3√125.2 as follows: Let f(x) = 3√x. The equation of the tangent line to f(x) at x=125 can be written in the form y=mx+b where m is ____ and where b is _____

Using this, we find our approximation for 3√125.2 is _____

(again, all the 3√, the 3 is inside the v, not 3 times sqrt)

Answer 1

In general,
f(x) ≅ f(x0) + f'(x0)*(x-x0)
For
f(x) = ∛x
f(x) ≅ ∛x0 + (x-x0)/(3∛(x0²))
Let x0=125, x=125.2
f(125.2) = f(125) + (125.2-125)/(3∛(125²))
=5 + (0.2)/(3*25)
=5.0267
Check: 5.0267³ = 125.2001...

Answer 2

So, m and b are?

Answer 3

Nevermind, got it.