Make the curve y=ax³+bx²+cx+d have a critical point at (0,-2) and also be a tangent to the line 3x+y+3=0 at (-1,0).

Francis June E. Seraspe's picture

Make the curve y=ax³+bx²+cx+d have a critical point at (0,-2) and also be a tangent to the line 3x+y+3=0 at (-1,0).
Ans nya po is y=x³+3x²-2. Salamat po

Jhun Vert's picture

Substitute (0, -2) to the given
Result: d = -2
 

Substitute (-1, 0) to the given
Result: -a + b - c = 1   ←   Eq. (i)
 

Differentiate
Result: y' = 3ax2 + 2bx + c   ←   Eq. (ii)
 

Set y' = 0 at (0, -2)
Result: c = 0
 

Differentiate the line
Result: y' = -3
 

Set y' = -3 at (-1, 0) to Eq. (ii)
Result: 3a - 2b = -3   ←   Eq. (iii)
 

Solve Eq. (i) and Eq. (iii) to find a and b.
 

Francis June E. Seraspe's picture

-a+b-c=2 po sir sa Eqn 1. D=-2 po.

Thanks sir

Francis June E. Seraspe's picture

D ko po makuha values nila sir.

Francis June E. Seraspe's picture

Nakuha ko na po sir. Salamat po

Jhun Vert's picture

Di na ako nag double check sa solution. I-comment mo lang sa post mo kung nakuha mo ang tamang equation.

Francis June E. Seraspe's picture

Nakuha ko na po sir. Salamat po

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