Why does the MC curve have the slope (positive, flat, or negative) it does?
473488
Assuming that C is the number of croissants produced, \nand w = wage per minute,\n\nTotal Cost is:\nTC =  w x (3.5xCxC) \n\nSo, Marginal Cost (the slope of the Total Cost curve) is:\nMC = w x 2x(3.5xC) = 7w x C\n\nThe MC has a positive slope equal to 7 times the wage per minute. This is because each croissant takes 7 minutes more than the last one to produce, and so costs more in wages...
802801
i think -1; y=mx+b, "b" is the 3 and "m"(slope) is negative one.
15640
In basic calculus, we use the derivative to find the slope of a curve, and the integral to find the area under a curve.  The question is, why are these operations the opposite of each other?\n\nThe quick answer is:  The derivative is used to calculate the rate of change of a function.  And the rate of change of the area under a curve is actually the original function.\n\n\nLet's say you have a simple curve, y=f(x).\n\nThe derivative of the function is gives you the rate of change of that function.  As x increases by 1, how much does y change?  That's also known as the slope.\n\n[And you probably know that the derivative of the derivative is also useful.  That's the rate of change of the slope.  When the slope stops changing (or its rate of change=0), it's at a maximum, minimum, or point of inflection.]\n\nThe same relationship exists for the area under a curve and the function itself.  You probably learned to think of the integral of f(x) as the sum of the thin vertical strips under the curve.  That's the area under the curve.  As you move to the right, how fast does the area grow?  You're essentially adding these vertical strips to the area.  The length of a vertical strip is f(x), or the original function.  So the original function f(x) represents how fast the area grows for any value x.\n\n\nETA: What do I have to do to get selected as best answer?
1095247
For a fixed a and n, and allowing b and c to vary, the curve would be a hyperbolar centered at the origin. You will only be taking the rational points on that curve, though.
900736
People are giving you conflicting information.  The answer is 2 when x>0.5 and -2 when x<0.5, but the important part is for you to be able to prove it to yourself.  Otherwise, when the test comes along, having just the answer to a different problem won't help.  Recognizing that the absolute value will give two answers is the first thing to remember, but it is also key to understand that it will create an reflection point of undefined slope.  The best way to understand this is to graph the equation y = abs(2x-1).  Simple plotting will show that the slope of the line is -2 until x=0.5, and 2 thereafter.  The key to finding this point of reflection is to set the absolute value equal to zero, not x equal to zero.\n\nYou should also realize that an equation could have more than one reflection point, as in abs(x^2 - 1), which has no definable slope at x = +/- 1, or abs(sin x), which has infinite slopeless points (one at each multiple of pi).  Just remember that every time the equation within the absolute value brackets crosses the x-axis with a non-zero slope, the derivative will be undefined.
751800
The 1st derivative is the slope of the original function.  If it is positive, you know the original function was rising (from left to right).  If it's positive but leveling off, the original still rising but not as much.  If it hits the x axis, there is a critical point on the original function (relative max/min or inflection point).
283222
Find the derivative to get an equation for the slope and then analyze it.  If you have a positive slope for the entire range that means your slope is greatest at the highest value.  If you want to know whether or not the slope goes up and down in your range, set the derivative to zero and solve.  If any of those zero values fall within your range (no), it means that the slope has changed directions and either gone up or down.  Use that answer to evaluate your equation.
407712
slope = -0.25\nintercept = 1
914585
f(x) satisfies the mean value theorem because it is continuous and differentiable on [-2, 1].\nSecant slope = (1 - 4) / (1 + 2) = -1\nDerivative f'(x) = 2x\n2x = -1\nx=-1/2 (this is what c equals to)
719360
It opens down because the coefficient of the x^2 term is negative.\nIf the parabola opens down, then the vertex will be a maximum.
533058
Point slope form:\n\ny-(-3)=(1/2)(x-5)
249704
Take the double derivative and find the inflection points. Analyze the behavior between the inflection points. If it is positive it is concave up. If it is negative it is concave down.
528541
The slope is zero, it is a horizontal line.  The equation is y=-3.\n\ny=mx+b is the slope intercept form where m is the slope and b in the place where the line crosses the y axis.\n\nSlope is rise over run. The is the difference in y's over the distance in x's.
1006269
Ok this is very simple. A positive slope means that an increase  in the NaCl or salinity of the bacteria culture increases the number of bateria cell count. A negative slope means that an increase in the salinity decreases the bateria cell count.\n\nI am assuming that you are ploting Salinity on the x-axis and Bateria Cell Count on the y-axis. This is based on your comment that NaCl is the independent variable and the Bateria Cell Count is the dependent variable.\n\nHowever, you were not clear on how time plays in this analysis. But I thought what would make sense is to plot time as the third axis (z-axis) as a second independent variable. So then you're also looking to see how Bateria Cell Count changes with time at a particular salinity. Hence you will get a 3-d plot with a 2-d surface for which you will need to calculate the slope.\n\nThis is a bit more complicated, but conceptually it is exactly the same as the 2-d case with just Salinity and Cell Count.\n\n----------------------------------------------------------------------------\n\nTried to reply to your email, but you're email is not confirmed with Yahoo. Anyways, to answer your question regarding dominance:\n\nThe slope is the indicator of dominance of one strain over another, i.e. the larger the slope value, the greater the dominance.\n\nFor references on "slope: see http://en.wikipedia.org/wiki/Slope
928890
The slope of a line can tell you how to get from one point on the line to another. If the equation is a linear equation, a straight line, then just by knowing one point and the slope you can graph the function because the slope will tell you how to get to the second point you need.\n\nFor instance, if you are told that a line goes through the point (0,2) and has a slope of 1/2 you can plot the second point and connect the dots to draw your line. Since the slope is "rise/run" you have to "rise" one and "run" two to get to another point. "Rising" 1 from 0 gets you to 1, and "running" 2 from 2 gets you to 4. So the next point is (1,4).\n\nIn a more general sense, the slope of a of a graph tells you how quickly the function is increasing or decreasing. For instance, the function f(x) = x^2 has a slope of 2x (trust me on this) where as the function g(x) = 2x^2 has a slope of 4x. What this means is that g(x) increases twice as quickly as f(x). If you look at these two lines on the same graph, it is evident that one increases much more quickly than the other.\n\nIf you progress on into higher mathematics courses, you will see how important the concept of the slope is, especially in Calculus.
599765
When graphed, a linear equation will form a straight line while a non linear equation will not be a straight line
346163
It's curved. Take Newton's second law F=ma, therefore m is proportional to 1/a and therefore the graph will be similar to a y=1/x graph and will be curved.\n\nTake F=ma, so m=F/a, proportionality is about if you double one thing the over doubles, however this is inversely proportional so if you double m you get a half of a, this is assuming that F is a constant.