Given f(2)=3 and f'(2)=0.4, Approximate f(2.2)

[dagr8est]

Given f(2) = 3 and f'(2) = 0.4, approximate f(2.2)

Could someone explain how to do this? Any help would be appreciated.

 

[stapel]

I would assume the instructions said something along the lines of "approximate the following value by using differentials"...?

What formula(s) did they give you to use? How far have you gotten in plugging the listed values into the formula(s)?

Please reply with specifics. Thank you.

Eliz.

 

[dagr8est]

No formulas were given. It just says the function f(x) is smooth. I haven't made any progress because I don't know how to start but I'd like to learn.

 

[skeeter]

use the equation of the line tangent to the curve of f(x) at (2,3) to approximate f(2.2).

the result is called a linear approximation.

 

[galactus]

Oops

 

[pka]

Sometimes this is called ‘linear approximation’, ‘linearization’ or some such.
Look for this topic in your textbook.
\(\displaystyle \L f(x + h) \approx (h)f'(x) + f(x).\)