Questions: Evaluate and simplify the difference quotient of the function f(x)=-6x-1 (f(x+h)-f(x))/h = □

Evaluate and simplify the difference quotient of the function f(x)=-6x-1 (f(x+h)-f(x))/h = □
Transcript text: Evaluate and simplify the difference quotient of the function $f(x)=-6 x-1$ \[ \frac{f(x+h)-f(x)}{h}=\square \] Question Help: Video
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Solution

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Solution Steps

Step 1: Compute \( f(x+h) \)

Given the function \( f(x) = -6x - 1 \), we first compute \( f(x+h) \): \[ f(x+h) = -6(x+h) - 1 = -6x - 6h - 1. \]

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

Next, we find the difference \( f(x+h) - f(x) \): \[ f(x+h) - f(x) = (-6x - 6h - 1) - (-6x - 1) = -6x - 6h - 1 + 6x + 1 = -6h. \]

Step 3: Compute the difference quotient

Now, we compute the difference quotient: \[ \frac{f(x+h) - f(x)}{h} = \frac{-6h}{h} = -6. \]

Final Answer

The difference quotient simplifies to: \[ \boxed{-6} \]

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