#need help

62 messages · Page 1 of 1 (latest)

wooden latchBOT
low berry
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need help with this question please

raw sparrow
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You gotta look at the graphs given , if red graph is positive then the blue graph sould be increasing, if its negative should be decrasing

uncut plinth
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The graph given is for f'(x), the gradient of the curve you want.

What is f'(0)? What does this mean about f(x) at x = 0?

What about the solutions of f'(x) = 0? Significance?

For x > 0, we know f'(x) < something... what does this mean?

And for x < 0?

What is the symmetry of f'(x)? What does that suggest about f(x)?

Which options don't have any / all / some of these properties?

low berry
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ah okay

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is the answer h?

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its either h or c correct?

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or did i do something wrong

uncut plinth
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What must f'(x) be doing as x approaches zero for (c) and (h)? Which matches what f'(x) is shown to be doing?

low berry
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h

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correct?

uncut plinth
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No. For h, as x goes to zero, the slope goes to vertical and so f'(x) should increase or decrease without bound. But, f'(x) is zero, so the graph of y = f(x) is horizontal / stationary.

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As x increases from zero, f'(x) is negative (graph decreases) getting larger in magnitude (f(x) starts from horizontal and gets steeper, but then f'(x) returns towards zero , so f(x) flattens and approaches a horizontal asymptote

strong hamlet
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whoever invented this non-linear shiiii is evil bro

uncut plinth
strong hamlet
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what is differencial taltulus

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bro why do we need this

chilly fractal
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Optimisation problems

low berry
chilly fractal
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Try sketching out a graph of f(x) based on the given graph of f'(x)

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Then see which one of these line up the best

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Notice the graph of f'(x) has an x intercept at x=0

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This suggests that f(x) has a stationary point at 0,and that it is a maximum stationary point as the sign of the derivative changes from positive to negative

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This eliminates us down to a few options

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Then notice that for x<0, the f'(x) >0 and for x>0, f'(x)<0

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This should leave us with two choices

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Then notice how f'(x) is increasing, until a certain point on the left side of the graph

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This leaves one option remaining

low berry
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is it d?

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yea I think it’s either d or e

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but I don’t know, I don’t want to get the question wrong

chilly fractal
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I was a bit eepy

low berry
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its okay no worries

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so its not d or e right?

chilly fractal
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I'll just send a pic

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This point is an example of a maximum stationary point

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Transitions from a positive to negative gradient

low berry
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g

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right?

chilly fractal
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Well no

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Also notice how the derivative is initially increasing from the left side of the graph

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This tells us the graph must have a upwards curving arc

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Not a downwards curving arc

low berry
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oh ok

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the only graphs with a upwards arc is A and B

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so itd be one of those correct?

chilly fractal
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Uh no

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Partial graph of f(x) would look a bit like this

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Which graphs in the options matched the curve shown here at that region

low berry
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c looks similar to that

chilly fractal
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Yep

low berry
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it has the start of that

chilly fractal
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Correct

low berry
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so itd be c

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wow okay

chilly fractal
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Yes

low berry
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makes sense now