Consider the function

, which has derivative

.
The linear approximation of

for some value

within a neighborhood of

is given by

Let

. Then

can be estimated to be

![\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B63.97%7D%5Capprox4-%5Cdfrac%7B0.03%7D%7B48%7D%3D3.999375)
Since

for

, it follows that

must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function

. This means the estimated value is an overestimation.
Indeed, the actual value is closer to the number 3.999374902...
Subtract 6 from both sides, you get 1/3x=-14
Now multiply both sides by there, hence x=-42
hello!
so the difference is 101 and here is why!
you want to minus -1 from 100
100 - (-1)
but because it is a double negative it will become addition
100 + 1
so the difference is 101 feet
i hope this helped :)