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Chapter 2: Problem 126

If \(f(x)=3 x+7,\) find \(\frac{f(a+h)-f(a)}{h}\)

Short Answer

Expert verified
Therefore, \(\frac{f(a+h)-f(a)}{h} = 3\).

Step by step solution

01

Function Evaluation

Evaluate the function \(f(x) = 3x + 7\) at \(a + h\) and at \(a\), which gives us: \(f(a+h) = 3(a+h) + 7\), and also \(f(a) = 3a + 7\).
02

Compute the Difference

Compute the difference \(f(a+h) - f(a)\). This will give us \((3(a+h) + 7) - (3a + 7)\). Simplifying this, we get \(3h\)
03

Division by h

Finally, the result is divided by \(h\), which gives us \(\frac{3h}{h}\). Thus, \(\frac{f(a+h)-f(a)}{h} = 3\).

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