Question

Please help!!
*f(x)= x(x+6)^1/2 find two x intercepts.
Then show that f'(x)=0 at some point between the 2 x intercepts.
*Use mean value theorem for f(x)= x(x^2-3x+1) for interval [1,4]
I FOUND DERIAVITIVE WHICH IS 3X^2-6X+1.THEN?
*find all critical numbers find all intervals on which the function is increasing or decreasing. lable extrma.
I FOUND MY DERIVATIVE WHICH IS -32X/(X^2-16)^2
CRITICAL NUMBERS ARE 0,4 AND -4.
SO WHAT DO i DO NEXT

Answer 1

the two x intercepts are 0, and -6

set the derivative equal to zero, and find x

f'(x)=(x+6)^1/2 + x/2 *1/(x+6)^2=0
x+6 + x/2=0
3x=-12
x=-4

***
find f(1), and f(4)
f(1)=-1
f(4)=20
this means there is a zero between x=1,4

*****
I wonder on this third question what is the function? Putting parts of several qustion on one question is very confusing.

Answer 2

f(x)=x^2/x^2-16

Answer 3

i got this. thnks