Calculas and curve sketching (1 Viewer)

[Tabris]

Consider the curve y = x^4 - 4x^3
find coordinate of stat points
determine anture of these stat points
sketch the curve using the above information
for what values of x is the curve concave up



x^4 - 4x^3

y' = 4x^3 - 12x^2
y"= 12x^2 - 24x

for stat points

4x^3 - 12x^2 = 0

4x^2(x-3) = 0

x = 3 and 0 meaning (3,27) and (0,0)

at x = 3

y">0

at x = 0

y" = 0 (pt of inflection)

when the point of inflection is ar the origin i tested it using -0.5, 0, and o.5

when subbed into y', -0.5 and 0.5 both got a negative gradiant meaning horizontal point of inflection right?

12x^2 - 24x > 0

12x^2 > 24x

x >2 (divided both sides by 12x)

so therefore the curve is concave up when x > 2

but how could that be if the state point is at (3,-27)?

anyone know where i made a mistake? ta, thanks for your time

 

[CM_Tutor]

y = x⁴ - 4x³ = x³(x - 4)

X intercepts at x = 0 and x = 4.

Horiz POI at (0, 0)

Min TP at (3, -27)

Concave up for x < 0 and x > 2

Graph looks sort of like a concave up parabola, but with a horiz POI in its LHS arc

 

[Winston]

y = x⁴ - 4x³ = x³(x - 4)

X intercepts at x = 0 and x = 3.

Horiz POI at (0, 0)

Min TP at (3, -27)

Concave up for x < 0 and x > 2

Graph looks sort of like a concave up parabola, but with a horiz POI in its LHS arc

how come u can have a turning point at 3 as well as a intercept at 3 as well? :S... wouldn't that be weird... =\

 

[CM_Tutor]

how come u can have a turning point at 3 as well as a intercept at 3 as well? :S... wouldn't that be weird... =\

You're right, that should be intercept at x = 4. I've corrected the typo.

 

[Winston]

You're right, that should be intercept at x = 4. I've corrected the typo.

lol few i thought not sketching curves for so many mths have made me forgotten everything :|

 

[Tabris]

thx again cchamp