When is this curving up and curving down?

(x^2-24x+136)

I have the derivative, but now what? Its been a while since i did any calc.

(x^2-24x+136)

I have the derivative, but now what? Its been a while since i did any calc.

(x^2-24x+136)

I have the derivative, but now what? Its been a while since i did any calc.

when dy/dx is +ve, the gradient is positive, therefore the graph is curving up, and when dy/dx is negative, it's curving down

solve dy/dx = 0 to find turning points

solve dy/dx = 0 to find turning points

lol.## JoshP wrote:

when dy/dx is +ve, the gradient is positive, therefore the graph is curving up, and when dy/dx is negative, it's curving down

solve dy/dx = 0 to find turning points

I UNDERSTOOD THIS.## JoshP wrote:

dy/dx

THIS IS DIFFERENTIATION.

......right?

no, dy/dx is related to differential equations. Differentiation are terms "x dx"## Sir Schmoopy wrote:

I UNDERSTOOD THIS.## JoshP wrote:

dy/dx

THIS IS DIFFERENTIATION.

......right?

When the x^2 is positive, it's a smiley face, when x^2 is negative, it's a frown face.

To find when it's curving up or down, differentiate, in this case:

f(x) = (x^2-24x+136)

f'(x) = (2x-24)

And when f'(x) is negative, it's going down, when f'(x) is positive, it's going up.

To find when it's curving up or down, differentiate, in this case:

f(x) = (x^2-24x+136)

f'(x) = (2x-24)

And when f'(x) is negative, it's going down, when f'(x) is positive, it's going up.

*Last edited by Sydney (2008-11-19 12:30:34)*

dy/dx = f'(x) ....

find the second derivative f", if that's positive, the graph is concave up(smiley face)if it's negative, the graph is concave down

This## argo4 wrote:

find the second derivative f", if that's positive, the graph is concave up(smiley face)if it's negative, the graph is concave down

Curving up (which sounds more like concavity that increasing/decreasing) is f'', the second derivative

f'' is the rate of change of the gradient, i.e if f'' is +ve the curve is getting steeper, and if -ve, it's getting shallower## Winston_Churchill wrote:

This## argo4 wrote:

find the second derivative f", if that's positive, the graph is concave up(smiley face)if it's negative, the graph is concave down

Curving up (which sounds more like concavity that increasing/decreasing) is f'', the second derivative

Umm, no?## JoshP wrote:

f'' is the rate of change of the gradient, i.e if f'' is +ve the curve is getting steeper, and if -ve, it's getting shallower## Winston_Churchill wrote:

This## argo4 wrote:

find the second derivative f", if that's positive, the graph is concave up(smiley face)if it's negative, the graph is concave down

Curving up (which sounds more like concavity that increasing/decreasing) is f'', the second derivative

Positive means it is facing up... \/ like that, but a curve... and negative means it is facing down /\, like that.

When the first derivative is positive, the curve is sloping up i.e. /

When the first derivative is negative, the curve is sloping down i.e. \

When the second derivative is positive, the curve is concave up i.e. \_/

When the second derivative is negative, the curve is concave down i.e. /^\

When the first derivative is negative, the curve is sloping down i.e. \

When the second derivative is positive, the curve is concave up i.e. \_/

When the second derivative is negative, the curve is concave down i.e. /^\

what vub said## Winston_Churchill wrote:

Umm, no?## JoshP wrote:

f'' is the rate of change of the gradient, i.e if f'' is +ve the curve is getting steeper, and if -ve, it's getting shallower## Winston_Churchill wrote:

This

Curving up (which sounds more like concavity that increasing/decreasing) is f'', the second derivative

Positive means it is facing up... \/ like that, but a curve... and negative means it is facing down /\, like that.

Good thing I'm not continuing with AP math after the next semester. Im taking grade 12 math next semester in grade 11, and I'm going to skip calculus.

^ This is the correct answer## Vub wrote:

When the first derivative is positive, the curve is sloping up i.e. /

When the first derivative is negative, the curve is sloping down i.e. \

When the second derivative is positive, the curve is concave up i.e. \_/

When the second derivative is negative, the curve is concave down i.e. /^\

Which is what i said. We were talking about f'' and its exactly what i said it was, he said the same thing as me but included f' as well## JoshP wrote:

what vub said## Winston_Churchill wrote:

Umm, no?## JoshP wrote:

f'' is the rate of change of the gradient, i.e if f'' is +ve the curve is getting steeper, and if -ve, it's getting shallower

Positive means it is facing up... \/ like that, but a curve... and negative means it is facing down /\, like that.

For some reason i read this thread title as "Cactus help"

o.o

o.o

*Last edited by Mitch (2008-11-19 15:54:42)*

15 more years! 15 more years!

which is what i said## Winston_Churchill wrote:

Which is what i said. We were talking about f'' and its exactly what i said it was, he said the same thing as me but included f' as well## JoshP wrote:

what vub said## Winston_Churchill wrote:

Umm, no?

Positive means it is facing up... \/ like that, but a curve... and negative means it is facing down /\, like that.

we were all getting confused by our different wording, lulz

Well, if f'' is negative its not getting shallower, its facing the other way lol## JoshP wrote:

which is what i said## Winston_Churchill wrote:

Which is what i said. We were talking about f'' and its exactly what i said it was, he said the same thing as me but included f' as well## JoshP wrote:

what vub said

we were all getting confused by our different wording, lulz