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onegirl
 2 years ago
Draw the second derivative given the graph of function f below.
onegirl
 2 years ago
Draw the second derivative given the graph of function f below.

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0first derivative of a parabola is probably a line second derivative will therefore be a constant, aka a horizontal line

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1362594670556:dw how will i draw it on here?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595003756:dwLet's draw some tangent lines to get a feel for what is going on

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595106001:dwSee 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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595210278:dwCheck 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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595320296:dwHow about this tangent line, what is it's value?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1what is the slope of this tangent line i mean*

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595394811:dwyes good. so the VALUE of our derivative will be 0.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595424698:dwWhen we go towards the right, the slope becomes positive. So our point will be somewhere up in the positive area.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595476831:dwAs we go further to the right, our slope gets really positive, so the value of the first derivative will be very positive.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Ok let's draw a line connecting these points.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362595554967:dwI had to fix a couple of the dots :) lol

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay that makes sense now

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1So how about the second derivative. Hmmm

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Yes 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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1With 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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Just make sure that you draw your second derivative ABOVE the xaxis. That shows that the first derivative was positive.
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