Consider the following function.
f(x) = 14x + 1/x
(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)
x =

(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing:
decreasing:

(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum (x, y) =
relative minimum (x, y) =

Question

Consider the following function.
f(x) = 14x + 1/x
(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)
x =   


(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing:    	 
decreasing:    	 

(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum    	(x, y)	 = 	
relative minimum    	(x, y)	 =

anonymous · Answer

i took the first derivative, which is the quotient rule, i believe and i got: 14 + 2x^-3==>14+2/x^3....i don't know what to do next

anonymous · Answer

Hmmm your first derivative seems to be flawed a little remember the derivative of a quotient is
 Given that f(x) = g(x)/h(x)

$$f'(x) = \frac{ (h(x))(g'(x))-(h'(x))(g(x)) }{ (h(x))^2 }$$

anonymous · Answer

so in this case your derivative would be

$$f'(x) = \frac{ (x)(14)-(14x+1)(1) }{ x^2 }$$

anonymous · Answer

Does it make sense how I got that?

anonymous · Answer

yes it does, i was able to figure it out on my own but thanks