200 x 150 = 30,000 to purchase
200 x 175 = 35,000 when selling
35000 - 30000 is 5,000 capital gain
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
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...
^ means to the power of or exponent
logb(x) = y is b^y = x
To get a decimal form of a fraction, divide the numerator by the denominator.
7/8 = 0.875