Respuesta :
We have that the original function is the following:
[tex]f(x)\text{ = 3}\cdot x[/tex]Now we must calculate the following:
1. f (x+h)
[tex]\begin{gathered} f(x+h)\text{ = 3}\cdot(x+h) \\ f(x+h)\text{ = 3}\cdot x\text{ + 3}\cdot h \end{gathered}[/tex]2. f(x+h)-f(x)
[tex]\begin{gathered} f\text{ (x+h) - f(x) = 3}\cdot(x+h)\text{ - 3}\cdot x \\ f(x+h)\text{ - f(x) = 3}\cdot x\text{ + 3}\cdot h\text{ - 3}\cdot x \\ f(x+h)\text{ - f(x) = 3}\cdot h \end{gathered}[/tex]3. (f(x+h)-f(x))/h
[tex]\begin{gathered} \text{\lbrack}f(x+h)-f(x)\rbrack/h\text{ =}\frac{3\cdot(x+h)-3\cdot x}{h} \\ \text{\lbrack}f(x+h)-f(x)\rbrack/h=\text{ }\frac{3\cdot x\text{ +3}\cdot h\text{ -3}\cdot x}{h} \\ \text{\lbrack}f(x+h)-f(x)\rbrack/h=\text{ }\frac{3\cdot h}{h}\text{ } \\ \text{\lbrack}f(x+h)-f(x)\rbrack/h\text{ = 3} \end{gathered}[/tex]