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Svet_ta [14]
3 years ago
12

Find and simplify the difference quotient f(x + 1) – f(x) for the following function.

Mathematics
2 answers:
Umnica [9.8K]3 years ago
5 0

Answer:

  • f(x + 1) – f(x) = m

Step-by-step explanation:

Let's ignore the fact that m = 0.

<u>The difference is:</u>

  • f(x + 1) - f(x) =
  • m(x + 1) + b - mx - b =
  • mx + m - mx =
  • m

So the difference is m, whatever it's value is.

ra1l [238]3 years ago
3 0

In your situation you said that

  • f(x) = mx+b
  • m=0

Putting those together, you'd have f(x) =  b because 0\cdot x+b=b.

To evaluate the difference quotient, first find each piece on it's own:

  • f(x+1) = b because f(x) = b no matter what your x-value is.
  • f(x) = b

So putting those together:

     f(x+1) - f(x) = b-b = 0

Remember that the difference quotient is basically finding the slope of something.  Since you were given that the slope is 0, the difference quotient should work out to match that.

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Writing the slope-intercept form of a linear equation, we have:

y=mx+b

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Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.

Now, using the point (0, -4), we have:

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Given:

The product of \dfrac{9}{5} and 8\dfrac{1}{4} greater than 5.

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By how much the product of \dfrac{9}{5} and 8\dfrac{1}{4} greater than 5.

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