Question

A differentiable function has the property that f(5) = 4 and f'(5) = 3. What is the estimate for f(4.8) using the local linear approximation for f at x=5?

Answer 1

`f(4.8)~~3.4`

Explanation:

We know that, `f(x+deltax)~~f(x)+f'(x)*deltax.........(star)`

Letting, `x=5, and, x+deltax=4.8 rArr deltax=-0.2" in "(star)," we get,"`

`f(5-0.2)=f(4.8)~~f(5)+f'(5)(-0.2),`

`=4-3(-0.2)=4-0.6`

`"Therefore, "f(4.8)~~3.4`