Question

find each of the following for f(x)=6x + 5. (a) f(x + h) (b) f(x + h) − f(x) (c) \\(\frac{f(x + h) − f(x)}{h}\\) (a) f(x + h) = \\(\square\\)

Explanation:

Step1: Substitute x+h into f(x)

$f(x+h) = 6(x+h) + 5 = 6x + 6h + 5$

Step2: Compute f(x+h)-f(x)

$f(x+h)-f(x) = (6x + 6h + 5) - (6x + 5) = 6h$

Step3: Divide by h

$\frac{f(x+h)-f(x)}{h} = \frac{6h}{h} = 6$ (h≠0)

Answer:

(a) $6x + 6h + 5$
(b) $6h$
(c) $6$