I need to maximize $\displaystyle |a|+|b|+|c|$.

The conditions are:

- $\displaystyle a,b, \ \text{and} \ c$ are real numbers

- $\displaystyle |x|\leq 1 \ \text{and} \ |ax^2+bx+c|\leq 100$.

I don't think that

Code:

Maximize[{a*x^2 + b*x + c,
{Abs[x] <= 1 && a*x^2 + b*x + c <= 100 &&
Element[{a, b, c}, Reals]}},
{a, b, c, x}]

worked, since the first line doesn't seem to maximize the right thing.

This:

Code:

In[147]:=
Maximize[{a*x^2 + b*x + c,
{Abs[x] >= 1 && a*x^2 + b*x + c <= 100 &&
Element[{a, b, c}, Reals]}},
{a, b, c, x}]
Out[147]=
{100, {a -> 25, b -> 0, c -> 0, x -> -2}}

did not work because it didn't satisfy the condition that $\displaystyle |x|\leq 1$.

The closest I got was

Code:

Maximize[{Abs[a]+Abs[b]+Abs[c], {Abs[x] =< 1 && Abs[a*x^2 + b*x + c] <= 100 && Element[{a, b, c}, Reals]}}, {a, b, c, x}]

, but this gave me an error message.

Could someone please help me? Thanks!