Question

Consider the function f(x) = x² – 3x – 4 and complete parts (a) through (C). (a) Find f(a+h); f(a+h)-f(a) (b) Find (c) Find the instantaneous rate of change of f when a = 7. (a) f(a+h) = (Simplify your answer. Do not factor.)

Answer 1

(a)

`f(a+h)=a^(2) +2ah+h^(2) -3a-3h-4`

(b)

`f(a+h)-f(a)=2ah+h^(2) -3h`

(c)

`(df(a+h))/(dx) \left \{ { \atop {a=7}} \right. =2h+11`

Explanation:

(a)

Simply evaluate (a+h) in the function:

`f(a+h)=(a+h)^(2) -3(a+h)-4=a^(2) +2ah+h^(2) -3a-3h-4`

(b)

Evaluate (a) in the function:

`f(a)=a^(2) -3a-4`

Using the previous answers lets calculate f(a+h)-f(a)

`f(a+h)-f(a)=a^(2) +2ah+h^(2) -3a-3h-4-(a^(2) -3a-4)=2ah+h^(2) -3h`

(c) To find the rate of change of f(a+1) when a=7 we need to calculate its derivate at that point:

`(df(a+h))/(dx) \left \{ { \atop {a=7}} \right. =2a+2h-3=2(7)+2h-3=2h+14-3=2h+11`