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).

Submitted by Francis June E… on

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

Tags
Minima maxima

Jhun Vert Tue, 04/14/2020 - 08:38

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.