The function F is such that F(x)=(3x+2)^3-5 for x0. Obtain an expression for F'(x) and hence explain why F is an increasing function?

Question

The function F is such that F(x)=(3x+2)^3-5 for x>0. Obtain an expression for F'(x) and hence explain why F is an increasing function?

Stephen H. · Accepted Answer

F' = 3(3x+2)2 and is positive for all x  thus F is always increasing.

Yefim S. · Answer

F'(x) = 9(3x + 2)2 > 0 for x > 0 and because F(x) increasing on interval (0,∞)

The function F is such that F(x)=(3x+2)^3-5 for x>0. Obtain an expression for F'(x) and hence explain why F is an increasing function?