Question

The function f is such that f\[ f(x) = 3(x+2)^3 -5~~~for ~~x \ge 0\](i) Obtain an expression for \[f'(x)\] and hence explain why f is an increasing function.

Answer 1

@dpaInc

Answer 2

f'(x) = 9(x+2)²

since x>0
x+2 >0
9(x+2)² >0 so f'(x) >0
thus f is an increasing function

Answer 3

How did you get f'(x)?

Answer 4

the formula says:
\[(u ^{n})' = n(u ^{n-1})u'\]
so [ 3(x+2)^3 -5]'= [3(x+2)^3]' - (5)'
= 3(3)[(x+2)^(3-1)] * (x+2)' - 0
= 9(x+2)² (1)
= 9(x+2)²

Answer 5

you good?

Answer 6

Yup! :D