Answer to Question #1427 in Calculus for Lauren

Question

Derivative: g[sup](1)[/sup]= 3x[sup]2[/sup]-4x+1 and graph of g passes through point P(2,3). Find g(x).

Answer 1

Let's integrate g⁽¹⁾:
int(g⁽¹⁾) = x³- 2x² + x + C;
As the function passes through the point (2,3), we can find the constant C:
2³- 2*2² + 2 + C = 3
C = 3-2 = 1
Then
g(x) = x³- 2x² + x + 1.