HELP PLEASE! Find f ′(x) and Compare the graphs of f and f ′ and use them to explain why your answer is reasonable.

Question

1)f(x)= 3x+7/8x

f'(x)=?

2) f'(x) = 0 when f...

3) f' is positive when f...

4) f' is negative when f...

Answer 1

the graph of f(x) will look like f(x)=3x for large +/- x (that is slope will be positive)

and a little like f(x)=7/(8x) for small x (so a line is mixed with hyperbola)

f'(x)=3-7/(8*x²)

f'(x)=0 x=+/-√(7/24)

f'(x)<0 when -√(7/24)<x<√(7/24)

f'(x)>0 when x<-√(7/24) and when x>√(7/24)