Answer:
The estimate is,
f(117) = 56
Explanation:
We use the linear approximation,
L(x) = f(a) + f'(a)(x-a)
In our case,
x = 117,
a = 115
f(115) = f(a) = 50,
f'(a) = f'(115) = 3
Putting all this into the linear approximation equation, we get,
L(117) = f(115) + (f'(115))(117-115)
L(117) = 50 + 3(2)
L(117) = 56
Or, approximately,
f(117) = 56