Question

A UCF student has sampled a differentiable function f(t) at time t=1 and verified thatf(1)=3 & f′(1) = −2, but he needs to estimate the value of f(t) at t=1.2. Based on the information he has, what's the best linear approximation for f(1.2)?

Answer 1

Answer:

The value of $f(1.2)=y-f'(1.2)(x-1.2)$.

Step-by-step explanation:

According to the given problem the value of taken functions are,

$f(1)=3$ and $f'(1)=-2$

Then to estimate the value of f(t) at t=1.2, one can consider the equation of tangent line of the graph of f(x)  at a point x=a  is,

$y=f(a)+f'(a)(x-a)\hfill (1)$

wnere f(x) is differentiable at the point x=a.

From (1) we can get,

$f(a)=y-f'(a)(x-a)$

In the present problem a=1, and we know value of f(1) and f'(1).

Hence, at a=1.2 and after finding value of f'(1.2) one can easily find,

$f(1.2)=y-f'(1.2)(x-1.2)$

which will give the best approximation.