Let f(x) = 8x^3 - 4x^4 + 7. Find critical pts, intervals,...

[Mbandi]

Let f(x) = 8x^3 - 4x^4 + 7. Find:

(i) The x co-ordinates of all the critical points.
(ii) The intervals on which f(x) is increasing or decreasing [Draw a table of signs for f ' (x) ]
(iii) The nature of the critical points
(iv) The x-co-ordinates of the points of inflection (if any)
(v) The open intervals on which f(x) is concave up or concave down.

*****Thanks in anticipation******

 

[tkhunny]

This is your fourth post? I guess it is okay for you not to know that we expect to see your work. Now is the time to figure it out. Let's see what you get and we'll help you see where you wander off - If, indeed, you do wander off.

 

[Mbandi]

My attempt???

(i) f ' (x) = 24x^2 - 16x^3=0 at critical points

8x (3x - 2x^2) = 0

8x = 0

3x - 2x^2 = 0
x(3 - 2x) = 0

at x = 0 is one critical point

3 - 2x = 0
-2x = -3
at x= 1.5 is one critical point

(ii) f(x) increasing between interval x greater/equal to 0 and x less/equal to 1.5
f(x) decreasing where x is less than 0 or greater than 1.5

(iii) At the critical points f ' (x) changes sign

(iv) No points of inflexion because f ' (x) changes signs at f ' (x) = 0

Not sure of this though. Hence my request.
Cheers

 

[tkhunny]

No 2nd derivative?

Pretty good, but make sure you are right.