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

Question

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

Answer 1

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.

Answer 2

f(2) + 0.5f'(2) = 2.5 + (0.5)(-2.5) = 2.5 - 1.25 = 1.25, right? Thank you so much!

Answer 3

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.