Answer:
[tex]f(a) = 5a + 1[/tex]
[tex]f(a + h) = 5a + 5h +1[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x + 1[/tex]
Solving (a): f(a)
Substitute a for x in [tex]f(x) = 5x + 1[/tex]
[tex]f(a) = 5a + 1[/tex]
Solving (b): f(a + h)
Substitute a + h for x in [tex]f(x) = 5x + 1[/tex]
[tex]f(a + h) = 5(a + h) +1[/tex]
Open bracket
[tex]f(a + h) = 5a + 5h +1[/tex]
Solving (c): [tex]\frac{f(a + h) - f(a)}{h}[/tex]
In (a):
[tex]f(a) = 5a + 1[/tex]
In (b):
[tex]f(a + h) = 5a + 5h +1[/tex]
So:
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - (5a+1)}{h}[/tex]
Open bracket
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - 5a-1}{h}[/tex]
Collect Like Terms
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a- 5a+5h+1 -1}{h}[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5h}{h}[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]
