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)?

The value of .

Step-by-step explanation:

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

and

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,

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

From (1) we can get,

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,

which will give the best approximation.

step-by-step explanation: