app of calc q (1 Viewer)

[astroman]

find any turning points

 

[Menomaths]

y'=x^3 -3x^2

set y' = 0

x^3-3x^2 = 0

solve for x

 

[astroman]

thanks i was making a silly mistake by making 1/4 x 4 = 4 -.-

 

[Joshmosh2]

http://imgur.com/iVqgqAj

Generally, all 'turning point' questions follow the same process:
1. Differentiate
2. Let the derivative = 0
3. Solve for x
4. Sub x back into f(x) to find the coordinates

- If they ask for you to determine the nature, you can use either the table method or the second derivative. I can explain that to you through PM if you want.

 

[astroman]

thanks for the help

 

[astroman]

 

[integral95]

you need turning points

 

[astroman]

i got turning points, they are:

min
max

 

[Joshmosh2]

for a), it is inferred that you find the stat pts.
By differentiation, x = +- (root) 2
and y = (approx) -1.66 and 9.66 respectively

From here, you can already tell which ones are max and min, but to be sure, you can use the table method to determine the roots.

*Note that since it asks to sketch within the domain, you should also find the values for y when x = -3 and x = 3
*Also note the y and x intercepts

That should be enough to sketch the graph.

b) For this, you will have to determine the nature of your stat pts, using table method.
e.g. http://imgur.com/S5eepaX

 

[Joshmosh2]

for a), it is inferred that you find the stat pts.
By differentiation, x = +- (root) 2
and y = (approx) -1.66 and 9.66 respectively

From here, you can already tell which ones are max and min, but to be sure, you can use the table method to determine the roots.

*Note that since it asks to sketch within the domain, you should also find the values for y when x = -3 and x = 3
*Also note the y and x intercepts

That should be enough to sketch the graph.

b) For this, you will have to determine the nature of your stat pts, using table method.
e.g. http://imgur.com/S5eepaX

And your max pt will be your max value within the domain

 

[astroman]

And your max pt will be your max value within the domain

is the max value 6?

 

[dan964]

Finding turning points
Find y' by differentiation
For S.P y' = 0
Test y'' to determine whether a minimum or maximum point.
For inflexions point, y'' = 0 and the curve changes concavity (both are required by BOSTES)

Check y'' to check your turning points are not inflexion point e.g. the (0,0) turning point in y=x^4

So if y'' = 0 then make sure you check the behaviour of y' near the point to check it isn't actually a turning point. Do this by testing y' near the point provided you don't cross over or pick another turning point or discontinuities (e.g. asymptote).

Make sure to substitute your x values back in f(x) to get the y-value, if the question asks for the points.

 

[Joshmosh2]

is the max value 6?

Whoops, I made a slight error. When i said that your max sp would be the max value within your domain, i was incorrect. In this case, by testing values at the domain, x = 3 has the highest value, because f(3) = 13