gistfile1.txt

Wolfram Alpha input to get polynomial approximation to function on an interval

for example to approximate exp(x) with ax^2 + bx + 1 on [0,1]:

solve (partial derivatives wrt a,b of (integral of (exp(x)-(ax^2 +bx+1))^2 from 0 to 1)) for a,b

or properly:

Solve[ D[ Integrate[ (exp(x)-(ax^2 +bx+1))^2, {x,0,1} ], {{a,b}} ] = 0, {a,b}]

for some reason, only the first works in wolfram alpha? but it doesn't generalize to more variables
i think it's just a time thing, it appears to stop after the integral. dunno why writing it in mathematica syntax slows things down?
in the first one i think it makes a list of the partial derivatives, but in the second it's a vector

Solve[ Function[D[ Integrate[ (exp(x)-(ax^2 +bx+1))^2, {x,0,1} ], # ]/@{a,b}] = 0, {a,b}]

doesn't work either. in fact, Function[1+#]/@{0,1} doesn't work

i guess wolfram alpha just doesn't do everything mathematica does?