Question

Calculus 2

Answer 1

I'm certain it's not the first or the last

Answer 2

@zepdrix

Answer 3

Closed. Did you figure this one out already? :o

Answer 4

I don't think so. If you have any idea, please

Answer 5

Oh I see :)

Answer 6

Hmm I can't figure out what's going on with this one.
I'm thinking we could estimate the derivative at certain points like this:\[\Large\bf\sf f'(x_1)\quad\approx\quad \frac{f(x_1)-f(x_o)}{x_1-x_o}\]But the numbers aren't working out right.. hmmm

Answer 7

\[\Large\bf\sf f'(2)\quad\approx\quad \frac{f(2)-f(0)}{2-0}\]Solving for f(2),\[\Large\bf\sf f(2)\quad\approx\quad 2f'(2)+f(0)\]

Answer 8

But that gives us like ... 117 +_+ no bueno.. hmmm

Answer 9

Using Linear Approximation should give us:\[\Large\bf\sf f(2)\quad\approx\quad f(0)+f'(0)(2-0)\]\[\Large\bf\sf f(2)\quad\approx\quad 39+23\cdot2\quad\approx\quad 85\]

Answer 10

Hmm weird, I'm not sure how they want you to approximate this... any ideas Ralph? :[

Answer 11

XD

Answer 12

It seems like what they're doing is:\[\Large\bf\sf f(2)\quad\approx\quad f'(0)+2f(0)\quad=\quad 23+2\cdot39\quad=\quad 101\]Which is one of the options for the first approximation.
But it doesn't seem to make sense to me... Hmmmm.

Answer 13

@ranga :D

Answer 14

To get to f(x) from f'(x) we need to integrate f'(x) which is same as finding the area under the curve and adding it to f(0). f(2) = f(0 + area under the curve of f'(x) between x = 0 and x = 2.

Answer 15

So as OOPS posted earlier (and erased):\[\Large\bf\sf \int\limits_0^2 f'(x)\;dx\quad=\quad f(2)-f(0)\]Then solving for f(2),\[\Large\bf\sf f(2)\quad=\quad f(0)+\int\limits_0^2f'(x)\;dx\]And then we're uhh..... approximating this area how? Treating it as a rectangle or triangle or something maybe?

Answer 16

Maybe the average of lower and upper Riemann sum?

Answer 17

f(0) = 39
f(2) = 39 + 1/2 * (23+39) * 2 = 39 + 62 = 101.
23 * 2 is the lower bound of the area evaluated at the left end and
39 * 2 is the upper bound of the area evaluated at the left end and

Answer 18

Oh oh maybe this:Apply trapezoid rule to approximate?