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first derivative of a parabola is probably a line second derivative will therefore be a constant, aka a horizontal line
okay can u show it?
|dw:1362594670556:dw| how will i draw it on here?
|dw:1362595003756:dw|Let's draw some tangent lines to get a feel for what is going on
|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.
|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.
|dw:1362595320296:dw|How about this tangent line, what is it's value?
what is the slope of this tangent line i mean*
|dw:1362595394811:dw|yes good. so the VALUE of our derivative will be 0.
|dw:1362595424698:dw|When we go towards the right, the slope becomes positive. So our point will be somewhere up in the positive area.
|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.
Ok let's draw a line connecting these points.
|dw:1362595554967:dw|I had to fix a couple of the dots :) lol
okay that makes sense now
So how about the second derivative. Hmmm
it will be horizontal
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.
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|
Just make sure that you draw your second derivative ABOVE the x-axis. That shows that the first derivative was positive.