Find an equation for the horizontal tangent to the curve y=x-3root x

[r-soy]

Hi

a ) find an equation for the horizontal tangent to the curve y=x-3root x
b) What is range of values of values of curve's slope ?
c ) What is range of values of curve ?

number a already I solved but my queation now in b and c

-----

I try to solve
b)
to get curve's slope must derivatives
range of values of values of curve's slope is ( - infinity , 1 ]
becuse when we put ( 0 ) in curve's slope It will comw 1


c ) did here put zero in y=x-3root x


please help me .

 

[Mark44]

Hi

a ) find an equation for the horizontal tangent to the curve y=x-3root x

What does 3root x mean?

Does it mean $$\sqrt[3]{x}$$

or $$3\sqrt{x}$$
?

b) What is range of values of values of curve's slope ?
c ) What is range of values of curve ?

number a already I solved but my queation now in b and c

-----

I try to solve
b)
to get curve's slope must derivatives
range of values of values of curve's slope is ( - infinity , 1 ]
becuse when we put ( 0 ) in curve's slope It will comw 1

What did you get for the derivative of this function?

c ) did here put zero in y=x-3root x


please help me .

 

[r-soy]

I mean $$3\sqrt{x}$$

 

[r-soy]

I get for the derivative of this function?

3 X 1/2rootx

= 3/2rootx

 

[Mark44]

I get for the derivative of this function?

3 X 1/2rootx

= 3/2rootx

No, that's not the derivative of y = x - 3x^1/2