# 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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- 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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- Minima Maxima: y=ax³+bx²+cx+d

## Substitute (0, -2) to the

Substitute (0, -2) to the given

Result:

d= -2Substitute (-1, 0) to the given

Result: -

a+b-c= 1 ← Eq. (i)Differentiate

Result:

y'= 3ax^{2}+ 2bx+c← Eq. (ii)Set

y'= 0 at (0, -2)Result:

c= 0Differentiate the line

Result:

y'= -3Set

y'= -3 at (-1, 0) to Eq. (ii)Result: 3

a- 2b= -3 ← Eq. (iii)Solve Eq. (i) and Eq. (iii) to find

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

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

Thanks sir

## D ko po makuha values nila

D ko po makuha values nila sir.

## Nakuha ko na po sir. Salamat

Nakuha ko na po sir. Salamat po

## Di na ako nag double check sa

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

## Nakuha ko na po sir. Salamat

Nakuha ko na po sir. Salamat po