average slope find

Question

let f(x) = x sqrt x+7 . Answer the following questions

1. Find the average slope of the function f on the interval [ -7,0] . Average slope =
2. Verifty the Mean Value Theorem by finding a number c in ( -7,0 ) , such that f'(c)= m . Answer c=

Answer 1

f(x) = x√(x+7)

1. On the interval [–7,0] the average slope of f(x) =

f(0) = 0√(0+7) = 0

f(–7) = –7√(–7 +7) = –7√(0)= 0

So the average slope = 0

2. We're looking for a number c in (–7,0) such that f'(c) = 0.

f'(x) = 0 when 3x + 14 = 0 which means that x = –14/3

Since f'(–14/3) = 0 and –7 < –14/3 < 0

this verifies the Mean Value Theorem.