C3/4 differentiation help- rep pts offer!

Hi,

i cant get my head around how to find out if a stationary point is a max, min or pt of inflexion

eg

y= (2x-3)^6

dy/dx = 12(2x-3)^5

x= 3/2, therefore y= 0, but is it a max or is it a min, or pt of inflexion and how do you know ?

help would really be appreciated =]]]

rep will be given to the person who submits the most delicious answer

Reply 1

MaccyG

13

To work out Max or min you differentiate again and put your x value in. If it comes out positive it is min if it comes out negative it is maximum. 0 is pt on inflection.

Reply 2

Tommy Jay

OP

MaccyG

To work out Max or min you differentiate again and put your x value in. If it comes out positive it is min if it comes out negative it is maximum. 0 is pt on inflection.

i tried that b4, but im afraid it cant be right, as answers say (1.5,0) on curve is a min =[[

MaccyG

To work out Max or min you differentiate again and put your x value in. If it comes out positive it is min if it comes out negative it is maximum. 0 is pt of inflection.

Not always.

Reply 4

Tommy Jay

OP

Mr M

Not always.

PLEASE HELP ME NOBLE MATHEMAGICIAN

Reply 5

sheligalo

Tommy Jay

PLEASE HELP ME NOBLE MATHEMAGICIAN

Tommy Jay

PLEASE HELP ME NOBLE MATHEMAGICIAN

Using:

\frac{dy}{dx}=12(2x-3)^5

When x=3/2 you get 0, so pick 2 values either side.. i.e. 3/2+0.1 and 3/2-0.1 or something and see what the gradients are at these points. Then you can judge what kind of turning point it is.

Using the above suggested values you can see that the gradient is positive either side of the turning point therefore the function is increasing either side of the point. i.e. its a minimum

Reply 6

Tommy Jay

OP

sheligalo

Using:

\frac{dy}{dx}=12(2x-3)^5

When x=3/2 you get 0, so pick 2 values either side.. i.e. 3/2+0.1 and 3/2-0.1 or something and see what the gradients are at these points. Then you can judge what kind of turning point it is.

Using the above suggested values you can see that the gradient is positive either side of the turning point therefore the function is increasing either side of the point. i.e. its a minimum