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# Mathematica and derivatives

1) a) Write a function in Mathematica that defines
f(x) = (e^(&#8722;(x&#8722;a)2 ))((x &#8722; a)2 &#8722; (x &#8722; a)3)
"
(a is a parameter) both in standard
format and in pure functional format. Call the traditional form, ftrad, and the
the pure form, fpure. Test both cases to make sure they return the same answer
for similar arguments.

b) Using the traditional form, find the fifth derivative of the function in a).

c) Plot the fifth derivative of the function in a) from x = 0 to x = 10 letting
the parameter, a, equal 5. Note: you can use the command Plot[f[x],{x,a,b},
PlotRange " All] to see the entire range of the graph.

d) Find the indefinite integral of the function in a).

e) Take the first derivative of the function and then use Solve to find the
extremum's of the function in a). Note: e&#8722;(x&#8722;a)2 only tends to 0 as x"# so
one can divide e&#8722;(x&#8722;a)2 out of the expression to determine the extremum not
at #.

#### Solution Summary

This provides an example of working with Mathematica and derivatives.

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