Questions: Given the following function, determine the difference quotient, (f(x+h)-f(x))/h f(x)=-7x+7

Given the following function, determine the difference quotient, (f(x+h)-f(x))/h f(x)=-7x+7
Transcript text: Given the following function, determine the difference quotient, $\frac{f(x+h)-f(x)}{h}$ \[ f(x)=-7 x+7 \]
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Solution

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Solution Steps

To determine the difference quotient for the given function \( f(x) = -7x + 7 \), we need to follow these steps:

  1. Substitute \( x + h \) into the function to get \( f(x + h) \).
  2. Compute the difference \( f(x + h) - f(x) \).
  3. Divide the result by \( h \).
Step 1: Calculate \( f(x + h) \)

Given the function \( f(x) = -7x + 7 \), we first calculate \( f(x + h) \): \[ f(x + h) = -7(x + h) + 7 = -7x - 7h + 7 \]

Step 2: Compute the Difference \( f(x + h) - f(x) \)

Next, we find the difference: \[ f(x + h) - f(x) = (-7x - 7h + 7) - (-7x + 7) = -7h \]

Step 3: Divide by \( h \) to Find the Difference Quotient

Now, we divide the difference by \( h \): \[ \frac{f(x + h) - f(x)}{h} = \frac{-7h}{h} = -7 \]

Final Answer

The difference quotient is \[ \boxed{-7} \]

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