- #1
Mspike6
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Hello,
I got this lobe Curve sketching question on my assignment. i know most of it but i think i got the drevetive part wrong. anyway, i will write the whol question with all the soultions i reached.
1] Use the Funtion F(x) = x2-4 [tex]\sqrt{x}[/tex]
a) State the domain
b) Determine the intercepts.
c)Is the graph Symmetric about the X-axis or Y axis ?
d) Find the Asymptotes
e) where does the function increase ? where does the function decrease ?
f. Determine the Maximum and minimum values.
Please, if someone could tell me which part is wrong, and direct me in the right way!
Thank, you
I got this lobe Curve sketching question on my assignment. i know most of it but i think i got the drevetive part wrong. anyway, i will write the whol question with all the soultions i reached.
1] Use the Funtion F(x) = x2-4 [tex]\sqrt{x}[/tex]
a) State the domain
It's domain is set for all positive real numbers
b) Determine the intercepts.
X-Intercept.
x2-4 [tex]\sqrt{x}[/tex]=0
x4 - 16x=0
x=0 or x= [tex]\sqrt[3]{16}[/tex]
Y-intercept
y= (0)2-4(0)
Y intercept is 0
c)Is the graph Symmetric about the X-axis or Y axis ?
No, There is no symmetry since the equation will change if we replaced (x,y) by (-x,y) or (x,-y)
d) Find the Asymptotes
There is no Asymptotes
e) where does the function increase ? where does the function decrease ?
F(x) =x2-4x1/2
F'(c) = 2x-2x-1/2
The Function increases when F'(x) >0
2x-2x-1/2>0
2x-1/2(x3/2-1) >0
x > 0 or x > 1
The curve is Increaseing in (1, Invfinity)
The function Decreases when F'(x) <0
2x-2x-1/2<0
2x-1/2(x3/2-1) <0
x < 0 or x < 1
The curve is Decreasing (0, 1)
f. Determine the Maximum and minimum values.
From here it all start making no sens. that's why i think i made a mistake in the drevative process.
But to get the maximum and minimum, i think i should get the Critical Points[ F'(x) =0 ] and then test those points on the second drevative test,
If F''(x) > 0 Then x is a minimum
If F'' (x) < 0 then x is a maximum
If F'' (x) = 0 then the test failed.
I got F''(X) to be equal to 2+x-3/2
Please, if someone could tell me which part is wrong, and direct me in the right way!
Thank, you