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Homework Difference Quotient Practice Answers
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In worksheet on division, all grade students can practice the questions to divide the numbers and find out the quotient and remainder. This exercise sheet on division can be practiced by the students to get more ideas to learn to divide and verify the results.
In division by two-digit numbers we will practice dividing two, three, four and five digits by two-digit numbers. Consider the following examples on division by two-digit numbers: Let us use our knowledge of estimation to find the actual quotient. 1. Divide 94 by 12
In this article, however, we won't be looking at derivatives in particular. Instead, we will be looking at the difference quotient, which is a stepping stone to calculating derivatives of functions. The difference quotient allows us to compute the slope of secant lines. A secant line is nearly the same as a tangent line, but it instead goes through at least two points on a function.
As always, the best way to practice this is to take a look at some example problems. But, before we do that, make sure you're comfortable with some basic operations with functions by checking out our videos on function notation, dividing functions, composite functions, and the slope equation. Having mastery of all of these techniques will make learning how to use the difference quotient much much easier!
As you can see, when trying to sub in terms into the difference quotient formula, the first equation will be much easier than the second. This is because the second equation involves a lot more operations, and the addition of "h" into that mix makes errors much more likely. This will become more apparent as we get into some example problems.
In order to use the difference quotient, all we need to do is set f(a) equal to f(x), and make the necessary modifications to accommodate "h". It is very important to keep track of what is in the parentheses, as this is where it is most common to make mistakes! Once we do all this, we simply substitute what we need from f(x) to set up the difference quotient.
Polynomial functions are of similar difficulty when it comes to finding the difference quotient. Again, as the degree (the highest exponent) of the polynomial gets higher, as does the difficulty. The most common difference quotient problems will deal with quadratic polynomial functions that have a degree of 2. Later, we will also look at a higher degree polynomial function by setting up a difference quotient for a cubic function.
Again, in order to use the difference quotient, all we need to do is set f(a) equal to f(x), and make the necessary modifications to accommodate "h". Also remember it is very important to keep track of what is in the parentheses, as this is where it is most common to make mistakes! As an important side note, make sure you tackle these kinds of problem when the function is expanded out fully! If this function had been in factored form, it would have been much harder to set up the quotient.
Just like with the quadratic function in the previous example, in order to use the difference quotient, all we need to do is set f(a) equal to f(x), and make the necessary modifications to accommodate "h". Also remember it is very important to keep track of what is in the parentheses, as this is where it is most common to make mistakes! This cannot be more important as we start dealing with more difficult equations and functions. Finally, just like the last example, make sure you set up the difference quotient for the function in its fully expanded form, i.e. not factored!
Once we have set up the difference quotient, all we need to do is expand whatever is in the brackets, collect like terms, and simplify! This is much more difficult compared to the quadratic example, as we have many more terms! Be sure to double and triple check your work. It is very easy to lose track of terms in these kinds of questions.
Polynomials and linear functions are often the simplest functions to deal with when doing problems on the difference quotient. The next sections cover rational and radical functions, which involve an extra level of difficulty. 2ff7e9595c
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