# Math Help - the derivative at a point

1. ## the derivative at a point

i need some help on estimating a value...the problem is

suppose that f(x) is a function with f(380)=16 and f`(380)=8, then it says to estimate f(383)

2. They give you f(380)=16, a.k.a. they've given you a point (x,y). They also give you f'(380)=8, so you know the slope of the tangent at that point.

Since we're estimating, you have three points and the slope, which give you enough information to estimate the fourth point.

(y1-y2)/(x1-x2) = m

Plug in and solve for the y value which is f(383).

At least, I think that's what they want you to do.

3. Here is a general approximation: $f\left( {x + \Delta x} \right) \approx f(x) + \left( {\Delta x} \right)f'(x)$.
Thus, $f(383) \approx f(380) + \left( 3 \right)f'(380)$.