Posted by **Z32** on Monday, September 28, 2009 at 6:25pm.

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)

- Calculus -
**MathMate**, Monday, September 28, 2009 at 8:14pm
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...

- Calculus -
**Z32**, Tuesday, September 29, 2009 at 12:55am
So, m and b are?

- Calculus -
**Z32**, Tuesday, September 29, 2009 at 3:45am
Nevermind, got it.

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