# the derivative at a point

• September 10th 2007, 11:27 AM
mer1988
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)
• September 10th 2007, 01:51 PM
ten_twentyfour
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.
• September 10th 2007, 02:32 PM
Plato
Here is a general approximation: $f\left( {x + \Delta x} \right) \approx f(x) + \left( {\Delta x} \right)f'(x)$.
Thus, $f(383) \approx f(380) + \left( 3 \right)f'(380)$.