Posted by **PLEASE HELP** on Thursday, May 31, 2012 at 3:20pm.

If f(2) = 2.5 and f'(2) = -2.5, then f(2.5) is approximately...

I have no idea how to do this without an equation.

- Calculus First Derivatives -
**MathMate**, Thursday, May 31, 2012 at 3:57pm
Use linearization:

f(2.5) = f(2)+(2.5-2.0)*f'(2) (approx.)

=f(2)+0.5f'(2)

I'll let you complete the answer.

- Calculus First Derivatives -
**PLEASE HELP**, Thursday, May 31, 2012 at 4:46pm
f(2) + 0.5f'(2) = 2.5 + (0.5)(-2.5) = 2.5 - 1.25 = 1.25, right? Thank you so much!

- Calculus First Derivatives -
**MathMate**, Thursday, May 31, 2012 at 9:09pm
Correct.

The general formula for linearization is

f(x+h)=f(x)+hf'(x) (approximately)

In general, the smaller the value of h, the more accurate the answer would be.

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