Make the curve y=ax³+bx²+cx+d pass through the points (0,1)and (-3,7) and have a critical point at (-1,3)

Ans. y=-x³-4x²-5x+1

Thanks po

April 13, 2020 - 9:11am

#1
Francis June E....

Minima maxima: Arbitrary constants for a cubic

Make the curve y=ax³+bx²+cx+d pass through the points (0,1)and (-3,7) and have a critical point at (-1,3)

Ans. y=-x³-4x²-5x+1

Thanks po

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Steps:

Result:

d= 1.Result: -27

a+ 9b- 3c= 6.Result: -

a+b-c= 2.y'to zero. Because (-1, 3) is a critical point, replacexwith -1.Result: 3

a- 2b+c= 0.Paano ko po makuha yung value ni a at b?

Eqn.2 at eqn 3 nalang po natira.

0=0 po yung eqn.4

C=-3a+2b kasi value ni c. At sinubstitute ko sa eqn. 2-4

Eq. (2): -27a + 9b - 3c = 6

Eq. (3): -a + b - c = 2

Eq. (4): 3a - 2b + c = 0

Eq. (2) - 3*Eq. (3)

-24a + 6b = 0

6b = 24a

b = 4a

Eq. (3) + Eq. (4)

2a - b = 2

2a - 4a = 2

-2a = 2

a = -1

Thank you sir Alexander and Sir Jhun Vert