Question

) Consider f(x)=ax+xln(bx) for a>0, b>1, and x>1.


Find f′(x): f′(x)=


Based on your expression for f′(x), is f(x) increasing or decreasing? (Enter increasing or decreasing.)


(Be sure that you can see why this is true for all values x>1.)


Find f′′(x): f′′(x)=


Based on your expression for f′′(x), is f(x) concave up or concave down? (Enter up or down.)


(Be sure that you can see why this is true for all values x>1.)

Answer 1

f′(x)= a +ln(bx)+1, based on a>0, b>1, and x>1 f'(x) always will be greater than 0, so f(x) is increasing 

f′′(x)= 1/x, based on a>0, b>1, and x>1 f''(x) always will be greater than 0, so f(x) is concave up