I was looking for an answer to this question in the calculus section but I struggled to do so. I was wondering if anyone here could answer my question (or make a video on it). When you are given a function f(x) and then given another function g(x) = f(ax) where a is some constant (.5, 5, etc), how do the values for g(x), g'(x), and g''(x) relate to the values of f(x), f'(x), and f''(x)? Thanks!
Hi bildnera,
I think it depends very much on which function you have. I think it will have an other impact on f(x) = x² than on f(x) = 2x+1/x + 7x, for example.
If you are interested in a special type of equations, then take the overall equation of this type, for example f(x) = ax²+bx+c and some letter for your five in the equation above, for example z.
Then make the derivations of ax²+bx+c and a(z*x)²+b(z*x)+c and compare.
If you like, present your results here afterwards so that other people can learn from it, too!
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