Question

For f(x)=ax^2+bx^3, what is the ordered pair (a,b) if the point (-1,2) is an extrema of f(x)

Answer 1

Is this for calculus for for algebra?

I'm going to assume that you know calculus.

df
---- = 2ax + b must equal zero if (-1,2) is an extreme value of f(x).
dx

Thus, 2ax + b = 0, and 2ax = -b, or x = -b/(2a). This is the familiar "x-coordinate of the vertex of a parabola."

Here that x-value is -1, so -1 = -b/(2a). From this we get -2a = -b, or

b=2a

so the ordered pair could be (a, 2a).