Given f ( x ) = 1 x + 4 , find the average rate of change of f ( x ) on the interval [ 5 , 5 + h ] . Your answer will be an expression involving h .

Answer 1

find the average rate of change of function fx= x from x1=16 to x =121the average rate of change is. Simply your answer

Answer 2

average rate of change formula is : (f(b) -f(a)) / (b-a). So in this question a = 5, and b = 5+h.

So

f(a) = f(5) = 1*5 + 4 = 9

f(b) = f(5+h) = 1*(5+h) + 4 = 5+h+4

apply to formula we will have

(5+h+4 -9) / (5+h -5)

simplify

so average rate of change will be h/h = 1.

Or it can be done using the definition of the first derivative

(f(x+h) - f(x))/h

so f(x+h) is f(5+h) and f(x) is f(5) for this question