Functions (1 Viewer)

[gh0stface]

1.how do you prove a function is increasing for all x greater than or equal to 0.

let f(x) = sqr(x)

the solution just finds the deriviative, but how does it conclude its increasing for all values of x.


2. whats the difference between a horizontal point of inflexion and a point of inflexion.

this questions bothered me for a long time.

EDIT

3 (methanics question).

in physics the centripetal force is directed inwards towards the centre. yet for 4u mechanics its directed outwards??
anyone have an explanation?

 

[Timothy.Siu]

1.how do you prove a function is increasing for all x greater than or equal to 0.

let f(x) = sqr(x)

the solution just finds the deriviative, but how does it conclude its increasing for all values of x.


2. whats the difference between a horizontal point of inflexion and a point of inflexion.

this questions bothered me for a long time.

are u sure this is 4unit lol
well to find if its increasing i think u find the second derivative and if its positive then its increasing.
2. the different is one is horizonatal and the other one isn't
e.g. y=x^3 that has an obvious horizontal point of inflexion

 

[gh0stface]

^lol wtf. doesnt make sense

 

[conics2008]

he ghost face.. to prove a function is increasing or decreaing always go to the first dy/dx ??

when doing this make sure f'(x)=0 and go to second dy/dx and prove if it a max or min

 

[conics2008]

for your qustion above, yes u must find the dy/dx and find where is its minimum point hence its 0 =]

 

[gh0stface]

im not trying to find the turning points. the question just asks to "show that this curve is increasing for all x=>0"

the question im askin is how does the first deriviative prove that for all values for x it is increasing?

 

[conics2008]

yeh i know, your not finding the turning poitns because when u go to first dy/dx ur findin that the function is increaing. this is basic 2unit work..

if f'(x) >0 then the function is increaing..??

and when u sub in 0 that is when x=0 f'(x)=0 that means it starts increasing for x>0

get the bigger picture or is it just me ??

 

[Timothy.Siu]

im not trying to find the turning points. the question just asks to "show that this curve is increasing for all x=>0"

the question im askin is how does the first deriviative prove that for all values for x it is increasing?

are u serious? i hope ur not doing 4unit

 

[conics2008]

turning points mean your find the coordinate that is (x,y) here ur just proving that its an increasing function..

can someone else explain to him, because im always a shitty over the net, i need a paper and a pen.

 

[Timothy.Siu]

im not trying to find the turning points. the question just asks to "show that this curve is increasing for all x=>0"

the question im askin is how does the first deriviative prove that for all values for x it is increasing?

because if the derivative is positive the function is increasing

 

[gh0stface]

ye i get what u mean that by subbing a value > 0, the function is increasing as the gradient is > 0.

but i was askin how you know its for all values of x, since there r may be turnin points after x = 0


i suppose the bok did lim x-> infinity or somefin.....

 

[Timothy.Siu]

ye i get what u mean that by subbing a value > 0, the function is increasing as the gradient is > 0.

but i was askin how you know its for all values of x, since there r may be turnin points after x = 0


i suppose the bok did lim x-> infinity or somefin.....

then u find if theres any turning points,

 

[Mumma]

For f(x) = sqrt(x),
d f(x)/dx = 1/(2*sqrt(x))

Since the sqrt function only outputs positive values for real values of x > 0, the range of df(x)/dx does not include any negative numbers, So df(x)/dx > 0 for all x > 0.

 

[gh0stface]

ye, i was finkin dat, but the answer just jumped to the conclusion

 

[Mumma]

started editing my post before you posted ... read it again lol

 

[gh0stface]

Generally you'd have to point out that dy/dx is continuous, starts at a non-negative value and has no real roots in that region (so it never becomes negative). Sometimes it can be something simple, like dy/dx = e^x which is positive for all real x.

^

ye i get it now. there was this complex function, like 2 exponentials together, n i couldnt be bothered findin the stationary points.

 

[shanks27]

for your 3rd question- where does it say the centripetal force isn't inwards????? it is inwards, BUT if the object is in contact with a surface then there will be a reaction force outwards but the centripetal force is always inwards in maths and physics

 

[mick135]

1.how do you prove a function is increasing for all x greater than or equal to 0.

let f(x) = sqr(x)

the solution just finds the deriviative, but how does it conclude its increasing for all values of x.


2. whats the difference between a horizontal point of inflexion and a point of inflexion.

this questions bothered me for a long time.

EDIT

3 (methanics question).

in physics the centripetal force is directed inwards towards the centre. yet for 4u mechanics its directed outwards??
anyone have an explanation?

(i haven't been bothered to look and see what questions have been answered, so i'm just answering all of them)

1- it helps to know what the graph looks like. so when it says its "increasing" - it means that it's value for f(x) is getting larger (which it is). so a good way to show this is to just differentiate, and show for values >= 0 its increasing.

2 - A horizontal point of inflexion is where the second derivative ='s 0. In other words, when you draw tangents to the curve - this tangent is flat (thus, horizontal) - don't confuse with critical points!

3 - centripical force is normally/always directed inwards. Its just simple vectors that show that. There could be a resistance force (friction) pushing it outwards though