So if the tangent is positive, the slope is positive- the curve is increasing. It sounds to me as though you’re lacking in a basic understanding of what those things mean.į’(x) is the derivative, the slope of the tangent to the curve at that point. I HAVE to draw the derivative charts to see the relationships! What do the zeros of the f’ graph mean to the f graph? Or to the f’’ graph? I don’t know!" You wrote: " I can’t see the relationships between f, f’, f’’, and f’’’ on the graph alone. It’s been 20 years since I taught calc, so bear with me: And I’m still in the middle of college apps. Where do I go from here? The class is not going to slow down. And there are no opportunities for re-tests. I just don’t have that interpretive sense that others in my Calculus class have, and my GPA is going to suffer because of it. I don’t take failure very well, as you saw. There was no way I could even BS the questions since I HAD to show work to get any credit! There’s no way I’m getting a B in that test. I HAVE to draw the derivative charts to see the relationships! What do the zeros of the f’ graph mean to the f graph? Or to the f’’ graph? I don’t know!Īnd even if I do do it this way, the test took way too long for me to finish. Why is it so easy to so many other people but ridiculously difficult to me? I can’t see the relationships between f, f’, f’’, and f’’’ on the graph alone. So negative 2 is less than orĮqual to x, which is less than or equal to 5.Just took the test on Curve Sketching and Interpreting Derivatives and now I’m mad and upset, so please excuse me if it sounds like I’m ranting. So on and so forth,īetween these integers. ![]() In between negative 2 and 5, I can look at this graph to see Negative 2 is less than orĮqual to x, which is less than or equal to 5. What is its domain? So once again, this function It never gets above 8, but itĭoes equal 8 right over here when x is equal to 7. Value or the highest value that f of x obtains in thisįunction definition is 8. Or the lowest possible value of f of x that we get What is its range? So now, we're notįunction is defined. Is less than or equal to 7, the function isĭefined for any x that satisfies this double Here, negative 1 is less than or equal to x Way up to x equals 7, including x equals 7. So it's defined for negativeġ is less than or equal to x. This function is not definedįor x is negative 9, negative 8, all the way down or all the way What is its domain? Well, exact similar argument. Is less than or equal to x, which is less thanĬondition right over here, the function is defined. So the domain of thisĭefined for any x that is greater than orĮqual to negative 6. ![]() Wherever you are, to find out what the value of It only starts getting definedĪt x equals negative 6. It's not defined for xĮquals negative 9 or x equals negative 8 and 1/2 or Is equal to negative 9? Well, we go up here. We say, well, what does f of x equal when x ![]() ![]() Is the entire function definition for f of x. Right over here, we could assume that this What is its domain? So the way it's graphed One more point (0,6) would give 6>3 which is a true statement, and shading should include this point. If point is (1,5) you can do the same thing, 5 > 5, but this would be right on the line, so the line would have to be dashed because this statement is not true either. If you try points such as (0,0) and substitute in for x and y, you get 0 > 3 which is a false statement, and if you did it right, shading would not go through this point. So lets say you have an equation y > 2x + 3 and you have graphed it and shaded. The has to do with the shading of the graph, if it is >, shading is above the line, and ). Without the "equal" part of the inequality, the line or curve does not count, so we draw it as a dashed line rather than a solid line The "equal" part of the inequalities matches the line or curve of the function, so it would be solid just as if the inequality were not there.
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