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).

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Francis June E....
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).

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
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....
Francis June E. Seraspe's picture

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

Thanks sir

Francis June E....
Francis June E. Seraspe's picture

D ko po makuha values nila sir.

Francis June E....
Francis June E. Seraspe's picture

Nakuha ko na po sir. Salamat po

Jhun Vert
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....
Francis June E. Seraspe's picture

Nakuha ko na po sir. Salamat po

 
 
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