In calculus, the derivative of a function is “a measure of how a function changes as its input changes” (Wikipedia). For example, if an object is traveling at a constant velocity, that velocity is the same from moment to moment, so the derviative is zero. If an object is falling, its velocity changes a little bit as the object starts falling, and then falls faster and faster as time goes by.
You can calculate the rate of change of a function by calculating:
(f(x + delta) - f(x)) / delta
, where delta
is the interval
between measurements. As delta approaches zero, you get closer and
closer to the true value of the derivative.
Write a module named Calculus
with a function derivative/2
. The
first argument is the function whose derivative you wish to find, and the
second argument is the point at which you are measuring the derivative.
What should you use for a value of delta
? I used 1.0e-10
, as that is a small
number that approaches zero.
Here is some sample output.
iex(1)> c("calculus.ex") [Calculus] iex(2)> f1 = fn(x) -> x * x end #Function<erl_eval.6.17052888> iex(3)> f1.(7) 49 iex(4)> Calculus.derivative(f1, 3) 6.00000049644222599454 iex(5)> Calculus.derivative(fn(x) -> 3 * x * x + 2 * x + 1 end, 5) 32.00000264769187197089 iex(6)> Calculus.derivative(&:math.sin/1, 0) 1.0
f1
function works.
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