Answer:
(a)
[tex]f(a+h)=a^{2} +2ah+h^{2} -3a-3h-4[/tex]
(b)
[tex]f(a+h)-f(a)=2ah+h^{2} -3h[/tex]
(c)
[tex]\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2h+11[/tex]
Step-by-step explanation:
(a)
Simply evaluate (a+h) in the function:
[tex]f(a+h)=(a+h)^{2} -3(a+h)-4=a^{2} +2ah+h^{2} -3a-3h-4[/tex]
(b)
Evaluate (a) in the function:
[tex]f(a)=a^{2} -3a-4[/tex]
Using the previous answers lets calculate f(a+h)-f(a)
[tex]f(a+h)-f(a)=a^{2} +2ah+h^{2} -3a-3h-4-(a^{2} -3a-4)=2ah+h^{2} -3h[/tex]
(c) To find the rate of change of f(a+1) when a=7 we need to calculate its derivate at that point:
[tex]\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2a+2h-3=2(7)+2h-3=2h+14-3=2h+11[/tex]
