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masha68 [24]
3 years ago
9

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 e

stimate 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)?
Mathematics
1 answer:
Paladinen [302]3 years ago
6 0

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.

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