# Minima maxima

## Critical points

May answer key po ba kayo nito. Icheck ko lang po sana kung tama answers ko. Thank you po. Critical points/maxima and minima

y=4-6x+x²

y=(2x-1)²

y=2+12x-x³

y=x³-3x²-9x+20

y=x³-3x²+4x+5

y=x³-6x²+12x

y=x⁴+2x²+8x+3

y=16x+4x²-x⁴

y=x²(x-2)²

a³y=x⁴

9a³y=x(4a-x)³

a³y=x²(2a²-x²)

a³y=x³(4a-3x)

a⁵y=x⁴(3a²-2x²)

## 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

## 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

## Minima Maxima: y=ax³+bx²+cx+d

What is the condition that the cubic y=ax³+bx²+cx+d shall have two Extremes?

Answer nya po is b²-3ac>0

Salamat po.

## Minima Maxima: 9a³y=x(4a-x)³

Patulong po ulit ako mam/sir

Yung process po sana ulit

9a²y=x(4a+x)³

Yung ans nya po is (a,3a) maximum

Thanks in advance mam/sir