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Re: Which of the following is a possible equation for the above graph? [#permalink]

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10 Aug 2009, 21:00

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The graph is a plot of y=f(x) ,which we have to find. Look at the graph closely. The graph cuts at (0,0)

So when x=0, y =0 . This eliminates option B and E. When you substitute 0 in option B, y= x^3 - 1, if x=0 -> y=0^3 -1 =-1. The corresponding co-ordinate is 0,-1 which is not the case with the graph

When you substitute 0 in option E , y= x^3+3x^2-x+2 , if x=0 y= 2. Again, the corresponding co-ordinate is 0,2 which is not the case.

Now we are left with options A,C and D.

In A, y =x^3. If x>0, y should be greater than 0. But this is not the case in the given graph. The graph has points in 4th quadrant which is (x,-y). So option A can be ruled out.

Now consider C , y=3x^3 + 2x. Again if x>0 , y should be greater than 0. Ex. if x=1 , y= 5. if x=1/10 , y = 0.003+ 0.2 = 0.203. But this is not the case in the given graph. The graph has points in 4th quadrant which is (x,-y). So option C can be ruled out.

Now consider D, y= 3x^3 -2x , In this case , for x>0 , y can be gretaer than 0 or less than 0. For ex, if x=1/10, y= 0.003-.02= -0.017. If x=1, y =1. For x=2, y=22. So for x> 0, Y can be less than or greater than 0, spanning I and IV quadrant. Therefore option D is correct.

Re: Which of the following is a possible equation for the above graph? [#permalink]

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11 Aug 2009, 01:14

D it is I don't think we can use the slope formula here... its a simple case of solving for X or Y and seeing the corresponding points on the graph.

What the source?
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Re: Which of the following is a possible equation for the above graph? [#permalink]

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11 Aug 2009, 02:14

Just use elimination, or substitution, when u sub in (0,0), u eliminate two choices, and when u sub in a small number, u elminate A and C. then u are left with D

Re: Which of the following is a possible equation for the above graph? [#permalink]

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23 Nov 2015, 09:28

Pretty sure calculus is not in the scope of the GMAT, so I apologize if this is a waste of time, but differentiation comes in handy here. There should be 2 points where the first derivative equals zero, i.e. a quadratic equation with 2 distinct roots for the local minima and maxima. This rules out A,B,and C. To decide between D and E, we apply second order conditions;we know that there is one inflection point at the origin, therefore the second derivative must = 0 where x = 0. For D, we have dy/dx = 9x^2 - 2; d2y/dx2 = 18x = 0, gives x=0, as required. Choose D. For E, we have dy/dx = 3x^2+6x-1. d2y/dx2 = 6x+6 =0. x is not 0. The answer is D

The graph shows that at x=0, y=0. Putting the value of x=0 in the above 5 equation will give that only A, C and D are left. B and E are out. Now we will have to calculate the slope. So using the concept of differentiation the formula for slope are as follows. A -> 3\(x^2\) C -> 9\(x^2\) + 2 D -> 9\(x^2\) - 2

From the graph we also know that the slope at x=0 is -ve Putting the value of x=0 in the above 3 equations, we get

A -> 3\(0^2\) --> 0 C -> 9\(0^2\) + 2 --> 2 D -> 9\(0^2\) - 2 --> -2

Only D satisfied the required condition,

Hence answer is D
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Which of the following is a possible equation for the above graph? [#permalink]

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25 Nov 2017, 12:10

A) x^3 B) x^3 -1 C) 3x^3 + 2x D) 3x^3 - 2x E) x^3 + 3x^2 - x + 2

one quick approach, i can think of,

First looking at the graph, there are up and downs, it means, there is no correlation between x and y. With this idea, let us attack the answer choices.

1.\(y = x^3\), when x is going to increase, y is also going to increase, there is co-relation, so this can't be the equation 2. \(y = x^3 -1\), when x is going to increase, y is also going to increase, there is co-relation, so this can't be the equation. 3. \(y = 3x^3 + 2x\), when x is positive, y is also positive, when x is negative, y is also negative, no chance of up and down, so this can't be the equation.

So left which D and E.

We can eliminate one of them, by looking at graph, if x = 0, then y = 0, only choice D satisfies.