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.
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
Thisargo4 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 shallowerWinston_Churchill wrote:
Thisargo4 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 shallowerWinston_Churchill wrote:
Thisargo4 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 saidWinston_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 shallowerWinston_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 answerVub 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 wellJoshP wrote:
what vub saidWinston_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 saidWinston_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 wellJoshP wrote:
what vub saidWinston_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 lolJoshP wrote:
which is what i saidWinston_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 wellJoshP wrote:
what vub said
we were all getting confused by our different wording, lulz