Annoying second derivative questions :( (1 Viewer)

[purplemoon]

I've been trying these questions for such a long time and dont even know the answers because there is no answer sheet attached !

QUESTION ONE:

The gradient function for a certain curve is given by dy/dx= (x+1)(x-2)(x-3)^2
a) State the abscissae of the stationary points
b) Investigate the nature of the stationary point at x=2

QUESTION 2:

if (second derivative)= 6x-8 and when x=0, y=1, (first derivative)= 7, find y as a function of x

please help !

 

[nightweaver066]

a) Abscissae = fancy word for x-value
Stationary points occur when dy/dx = o
x = -1, 2 and 3

b) Draw a table and have x = 2-, x = 2 and x = 2+ on the top row
Bottom row sub in the numbers and write down the values you get
2- means just a bit smaller than 2 so use 1.999
2+ means just a bit bigger than 2 so use 2.001
By examining the change in derivative, draw a mini diagram to visualise it to determine whether the stationary point is a maximum/minimum/(horizontal inflexion) point

2. y'' = 6x - 8
y' = integral of (6x - 8) dx
= 3x^2 - 8x + c
When x = 0, y' = 7
7 = 3 + 8 + c
c = -3
y' = 3x^2 - 8x - 3
y = x^3 - 4x^2 - 3x + c'
When x = 0, y = 1
1 = c'
.'. y = x^3 - 4x^2 - 3x + 1

I should not be doing this at this time....

 

[purplemoon]

Thanks so so so much, makes alot of sense- i really appreciate it greatly !!
All the best for your HSC- goodluck