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calculus differentiation

Another way to consider the differentiation is to explain it using graphs. Some functions have curved graphs. In these curved graphs, when x is increased by a small number dx, y can be increased or decreased (depends on the type of the equation) by dy. If we suppose that the amount of increment dx is so small that the curved pattern is almost the same as a straight line, then the ratio of the dy and dx is the slope of the curve. Although we found the slope of the curve, technically we didn't find the slope of the entire curve. Because a curved pattern graph, the slope is changing constantly the slope we found is technically the slope of the curve at a specific point. At specific point if curve is sloping upward by 45 degree dy/dx is one, steeper than 45 degree greater than 1, less steep than 45 degree less than 1. Some curved graphs have a combination of positive and negative slopes and the point where the sign of slope changes is called local minimum or local maximum. Also using the technique to find the differentiation, we can also find the slopes of curves by just looking at the equation.

We can also use the differentiation method to find when the y value reaches its maximum or minimum. Sometimes, when the maximum point or the minimum point, is a whole number it is easier to find the value. However, if the value is not the whole number it is much harder to find in a guess and check way. We can use the property from the last chapter to find out this value. Last chapter we learned that at maximum or minimum point the value of dy/dx equals 0. Therefore, if we know the equation of the function find the value of dy over dx which would be another equation contains x. Then set the latter equation equal to zero and solve for x. Then we can simply chug the x value to the original equation to find the y value. Then to determine whether the value is the minimum or the maximum, substitute a number very close to the x value and find y va…

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