Problem 126
Question
If \(f(x)=3 x+7,\) find \(\frac{f(a+h)-f(a)}{h}\)
Step-by-Step Solution
Verified Answer
The derivative of \(f(x) = 3x + 7\) using the difference quotient formula is 3.
1Step 1: Substitute f(a) into the expression
Substitute \(a\) into the function \(f(x) = 3x + 7\). This gives \(f(a) = 3a + 7\).
2Step 2: Substitute f(a+h) into the expression
Substitute \(a+h\) into the function \(f(x) = 3x + 7\). This gives \(f(a+h) = 3(a+h) + 7 = 3a + 3h + 7\).
3Step 3: Substitute f(a+h) and f(a) into the expression
Substitute \(f(a+h)\) and \(f(a)\) into the difference quotient formula \(\frac{f(a+h)-f(a)}{h}\). This gives \(\frac{3a + 3h + 7 - (3a + 7)}{h} = \frac{3h}{h} = 3\).
Other exercises in this chapter
Problem 122
Use transformations of the graph of the greatest integer function, \(f(x)=\operatorname{int}(x),\) to graph each function. $$h(x)=\operatorname{int}(-x)-1$$
View solution Problem 124
will help you prepare for the material covered in the next section. $$ \text { Solve for } y: 3 x+2 y-4=0 $$
View solution Problem 127
Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each orde
View solution Problem 128
If \(f(x+y)=f(x)+f(y)\) and \(f(1)=3,\) find \(f(2), f(3)\) and \(f(4) .\) Is \(f(x+y)=f(x)+f(y)\) for all functions?
View solution