anonymous
  • anonymous
Draw the second derivative given the graph of function f below.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
first derivative of a parabola is probably a line second derivative will therefore be a constant, aka a horizontal line
anonymous
  • anonymous
okay can u show it?

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anonymous
  • anonymous
|dw:1362594670556:dw| how will i draw it on here?
anonymous
  • anonymous
@zepdrix can u help?
zepdrix
  • zepdrix
|dw:1362595003756:dw|Let's draw some tangent lines to get a feel for what is going on
anonymous
  • anonymous
ok
zepdrix
  • zepdrix
|dw:1362595106001:dw|See how the SLOPE of the porabola is very negative on the left? The line is pointing downward, very negative. That line has a bad attitude! XD That is telling us that the VALUE of our first derivative will be very negative. I've drawn a point near the bottom to show this.
anonymous
  • anonymous
okay
zepdrix
  • zepdrix
|dw:1362595210278:dw|Check out this tangent line. It's still pointing downward, but not as much as the last one. It has a less negative slope. So our first derivative will have a negative value, but not as negative as the first point.
anonymous
  • anonymous
okay
zepdrix
  • zepdrix
|dw:1362595320296:dw|How about this tangent line, what is it's value?
zepdrix
  • zepdrix
what is the slope of this tangent line i mean*
anonymous
  • anonymous
0
zepdrix
  • zepdrix
|dw:1362595394811:dw|yes good. so the VALUE of our derivative will be 0.
anonymous
  • anonymous
okay
zepdrix
  • zepdrix
|dw:1362595424698:dw|When we go towards the right, the slope becomes positive. So our point will be somewhere up in the positive area.
anonymous
  • anonymous
okay
zepdrix
  • zepdrix
|dw:1362595476831:dw|As we go further to the right, our slope gets really positive, so the value of the first derivative will be very positive.
zepdrix
  • zepdrix
Ok let's draw a line connecting these points.
zepdrix
  • zepdrix
|dw:1362595554967:dw|I had to fix a couple of the dots :) lol
anonymous
  • anonymous
okay that makes sense now
zepdrix
  • zepdrix
So how about the second derivative. Hmmm
anonymous
  • anonymous
it will be horizontal
zepdrix
  • zepdrix
|dw:1362595623497:dw|
zepdrix
  • zepdrix
Yes good! Because the slope of this line is constant yes? If we were to check points, we would see that the tangent lines are all giving us the same slope.
anonymous
  • anonymous
yes
zepdrix
  • zepdrix
With the way I've drawn this particular first derivative, it has a slope of approximately 1. So our second derivative would have a VALUE of 1.|dw:1362595735329:dw|
anonymous
  • anonymous
ok
zepdrix
  • zepdrix
Just make sure that you draw your second derivative ABOVE the x-axis. That shows that the first derivative was positive.
anonymous
  • anonymous
okay thanks

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