Maxima and minima graph sketching (1 Viewer)

[gh0stface]

how do u draw this:

y=2x^3-9x^2+12
y=x^3-27x

how would u get the x and y intercept?

 

[Foxodi]

Find all Stationary points, Determine Nature
Find all points of inflexion
Find y-intercept (x-intercept not worth it imo)
Graph?.... table of values doesnt hurt either

 

[gh0stface]

the x intercepts was the problem.......the textbook also didnt giv answers... k fk it.

 

[PC]

y=2x³ – 9x² + 12
dy/dx = 6x² – 18x
d²y/dx² = 12x – 18

When x = 0, y = 12
.: y-intercept at (0,12)

When dy/dx = 0, 6x² – 18x = 0
6x(x – 3) = 0
x = 0 or 3
When x = 0, y = 12 and d²y/dx² = –18
When x = 3, y = –15 and d²y/dx² = 18
.: Maximum turning point at (0,12)
.: Minimum turning point at (3,–15)

When d²y/dx² = 0, 12x – 18 = 0
12x = 18
x = 1.5
When x = 1.5, y = –1.5 and d²y/dx² changes sign through the point.
.: Point of inflection at (1.5,–1.5)


y=x³ – 27x
dy/dx = 3x² – 27
d²y/dx² = 6x

When x = 0, y = 0
.: y-intercept at (0,0)

When dy/dx = 0, 3x² – 27 = 0
3(x² – 9) = 0
3(x + 3)(x – 3) = 0
x = –3 or 3
When x = –3, y = 54 and d²y/dx² = –18
When x = 3, y = –54 and d²y/dx² = 18
.: Maximum turning point at (–3,54)
.: Minimum turning point at (3,–54)

When d²y/dx² = 0, 6x = 0
x = 0
When x = 0, y = 0 and d²y/dx² changes sign through the point.
.: Point of inflection at (0,0)


In both cases the x-intercepts are not nice rational numbers so as foxodi says, don't lose sleep. Remember this is just a sketch of a curve, not a work of art.