Question #1427

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

Expert's answer

Let's integrate g^{(1)}:

int(g^{(1)}) = x^{3}- 2x^{2} + x + C;

As the function passes through the point (2,3), we can find the constant C:

2^{3}- 2*2^{2} + 2 + C = 3

C = 3-2 = 1

Then

g(x) = x^{3}- 2x^{2} + x + 1.

int(g

As the function passes through the point (2,3), we can find the constant C:

2

C = 3-2 = 1

Then

g(x) = x

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