Draw the second derivative given the graph of function f below.

- anonymous

Draw the second derivative given the graph of function f below.

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- anonymous

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- anonymous

first derivative of a parabola is probably a line
second derivative will therefore be a constant, aka a horizontal line

- anonymous

okay can u show it?

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- anonymous

|dw:1362594670556:dw| how will i draw it on here?

- anonymous

@zepdrix can u help?

- zepdrix

|dw:1362595003756:dw|Let's draw some tangent lines to get a feel for what is going on

- anonymous

ok

- 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

okay

- 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

okay

- zepdrix

|dw:1362595320296:dw|How about this tangent line, what is it's value?

- zepdrix

what is the slope of this tangent line i mean*

- anonymous

0

- zepdrix

|dw:1362595394811:dw|yes good. so the VALUE of our derivative will be 0.

- anonymous

okay

- 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

okay

- 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

Ok let's draw a line connecting these points.

- zepdrix

|dw:1362595554967:dw|I had to fix a couple of the dots :) lol

- anonymous

okay that makes sense now

- zepdrix

So how about the second derivative. Hmmm

- anonymous

it will be horizontal

- zepdrix

|dw:1362595623497:dw|

- 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

yes

- 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

ok

- zepdrix

Just make sure that you draw your second derivative ABOVE the x-axis. That shows that the first derivative was positive.

- anonymous

okay thanks

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