Finding the relative max and min. 2 QUESTIONS

[yanarains]

I have 2 questions. First I want to just show my work to make sure that I am doing this right. I think I am but still not to sure.

Both questions need to find relative max and min:

1st question:
f(x)=x^3-12x^2
=3x^2-24x: f(x)=3x(x-8)
F(x)= 0 when x=8 and x=0

I find my intervals: x>8, 0<x<8, x<0
Test points: 9, 4, -2
f(9)=27>0 - increasing x>8
f(4)=-48<0 - decreasing 0<x<8
f(-2)=60>0 - increasing x<0

I then find my y-values for 8 and 0
f(8)= (8)^3-12(8)^2 = (8, -256)
F(0)= (0,0)
So then I have a relative min at (8,-256) and no extremum at (0,0).
If this is wrong could you please explain to me how exactly I can solve this type of problem.

2nd questions: same find max and min.

f(t)=3t^5-t^3-20 = 15t^4-3t^2 (I not sure if I am factoring this right would it be like 3t^2(5t^2 -1)) Is that right. I don't think so could you please give me a hint.

Thanks so much for your time!

 

[tkhunny]

f(x)=x^3-12x^2
=3x^2-24x: f(x)=3x(x-8)
F(x)= 0 when x=8 and x=0

I find my intervals: x>8, 0<x<8, x<0
Test points: 9, 4, -2
f(9)=27>0 - increasing x>8
f(4)=-48<0 - decreasing 0<x<8
f(-2)=60>0 - increasing x<0

I then find my y-values for 8 and 0
f(8)= (8)^3-12(8)^2 = (8, -256)
F(0)= (0,0)

You do seem to have the idea, but I'm going to pick on your notation quite a bit.

1) You start with f(x). That's fine.
2) You find the derivative, and call it f(x) also. This is confusing, if not generally incorrect.
3) Immediately, you abandon both those definitions and use F(x). This is confusing, if not incorrect.
4) While evaluating values of the derivative, you stick with f(x). This would be okay if you hadn't first defined f(x) as the original function.
5) While evaluating the original function, you use f(x) and F(x). Now you have the function and its derivative BOTH defined as BOTH f(x) and F(x).

Make up your mind. Upper case and lower case generally are not the same thing. f(x) and F(x) should signify different functions.

A derivative should not have the same definition as the function from whence it came. Often it gets a prime notation.

f(x) = x^3 - 12x^2 = (x-12) x^2
f'(x) = 3x^2 - 24x = 3(x-8)x
No "F(x)" in sight.

Be careful.
Notation matters.
Notation will help you if you are consistent.
Bad notation will confuse you.

 

[yanarains]

Sorry about that. Is the answer correct for problem 1 and still need help with the 2nd question. Thank you. Criticism is appreciated helps me get back on track. thanks!

 

[stapel]

Both questions need to find relative max and min:

1st question:
f(x)=x^3-12x^2 =3x^2-24x: f(x)=3x(x-8)
F(x)= 0 when x=8 and x=0

How did you get that x² - 12x² was equal to 3x² - 24x? Where is your derivative? How does F(x) relate to f(x)?

2nd questions: same find max and min.

f(t)=3t^5-t^3-20 = 15t^4-3t^2

With the second "equals" sign in there, are you sure you're supposed to be differentiating something, and not solving the equation 3t⁵ - t³ - 20 = 15t⁴ - 3t²?

Eliz.

 

[Deleted member 4993]

Sorry about that. Is the answer correct for problem 1 and still need help with the 2nd question. Thank you. Criticism is appreciated helps me get back on track. thanks!

The answer for problem number 1 is not correct, and we cannot fix it, because of the notation problem tkhunny mentioned