f(x)=x^3+bx^2+cx find b and c so that f has a critical number at (1,3)

Answer 1

In the given equation you can plug x=1 and f(x) =3

You get the equation b+c=2 --------- equation 1

At critical points the slope is either 0 or undefined.

To find the slope you can take the derivative of the given equation, then plugging x=1

you get the equation 2b+c= -3 --------equation 2



You now have two equations, You can use Elimination method to solve the two equations and get the values of b and c.

Answer 2

You have two equations and two unknowns:

Eqn 1 is 1³ + b*1² + c*1 = 3 f(1) = 3

Critical point: df/dx = 0 or goes to +/- infinity with the provision that the point exists in the domain of f. In this case,

Eqn 2 3(1)² +2*b*1 +c = 0 df/dx at x = 1 = 0

You can solve for b and c by substitution or Gaussian Elimination.

Please consider a tutor.