f(x)=6x-9 find f(a+h)-f(a)/h
You asked:
Evaluate the function \(f\left( x \right) = 6 x - 9\), \(f\left( a + h \right) - \frac{f\left( a \right)}{h}\).
MathBot Answer:
$$\begin{aligned}f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{6 a h - 6 a + 6 h^{2} - 9 h + 9}{h}\end{aligned}$$
$$\begin{aligned}f\left( a + h \right) - \frac{f\left( a \right)}{h}&=-9 + 6 \left(a + h\right) - \frac{-9 + 6 a}{h}\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{9 - 6 a}{h} + -9 + 6 \left(a + h\right)\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{9 - 6 a}{h} + 6 a + 6 h - 9\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{6 a h - 6 a + 6 h^{2} - 9 h + 9}{h}\\\end{aligned}$$