Given f(x) = 5x^3 - 15x^2, find zeroes, 1st & 2nd deriv, tangent at x = 3, etc.

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ubuntu

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Hello math people. I have a math question that am struggling with. could someone help me solve it and maybe explain how they came about the answer coz that would be very helpful in solving similar questions.

Given the function f(x)=5x3-15x2

A) When is f(x)=0?


B) Find f '(x) and f"(x)


C) Use the derivative and the 2nd derivative test to find and classify any local maximum and minimum points.


D) Find the equation for the tangent to f(x) when x=3.

I'd be most grateful if someone helped me out :)
 
ubuntu said:
Hello math people. I have a math question that am struggling with. could someone help me solve it and maybe explain how they came about the answer coz that would be very helpful in solving similar questions.

Given the function f(x)=5x3-15x2

A) When is f(x)=0?


B) Find f '(x) and f"(x)


C) Use the derivative and the 2nd derivative test to find and classify any local maximum and minimum points.


D) Find the equation for the tangent to f(x) when x=3.

I'd be most grateful if someone helped me out :)
Click to expand...

Hint: (A) Factorize f(x) → f(x)=5x3-15x2 → f(x) = 5x2(x-3) .... continue...

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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ok.. so here is what i have done so far

A) f(x) = 5x3-15x2 = 5x2 (x-3)

= ( I couldn't simply further than this )

B) f(x) = 5x3-15x2


  • f'(x) = 15x2-30x

  • f"(x)=30x-30

C) am not sure what to do here.help?

D) f(x) = 5x3-15x2

f(3)=5(3)3-15(3)2
f(x) =0
 
ubuntu said:
ok.. so here is what i have done so far

A) f(x) = 5x3-15x2 = 5x2 (x-3)

= ( I couldn't simply further than this )

B) f(x) = 5x3-15x2


  • f'(x) = 15x2-30x

  • f"(x)=30x-30

C) am not sure what to do here.help?

D) f(x) = 5x3-15x2

f(3)=5(3)3-15(3)2
f(x) =0
Click to expand...


A) f(x) = 5x3-15x2 = 5x2 (x-3)

f(x) = 0 → 5x2 (x-3) = 0

x2 (x-3) = 0 → x2 = 0 → x = 0 and ???
 
ubuntu said:
ok.. so here is what i have done so far

A) Solve f(x) = 0:

f(x) = 5x3-15x2 = 5x2 (x-3)

= ( I couldn't simply further than this )
Click to expand...
This was given to you. Now set f(x) equal to zero, as they specified (and just like you learned back in algebra), and solve the factors.

ubuntu said:
B) Find f'(x) and f"(x):

f(x) = 5x3-15x2


  • f'(x) = 15x2-30x

  • f"(x) = 30x-30
Click to expand...
Yes.

ubuntu said:
C) Use the First and Second Derivative Tests to find and classify any local maximum and minimum points.

am not sure what to do here.help?
Click to expand...
These Tests were supposed to have been covered in class, and should have comprised a major portion of an entire chapter in the textbook. To learn now about the First and Second Derivative Tests, please try here. After you have studied at least two lessons from the listing, please attempt this portion of the exercise.

ubuntu said:
D) Find the equation for the tangent to f(x) when x = 3.

f(x) = 5x3-15x2

f(3)=5(3)3-15(3)2
f(x) =0
Click to expand...
Okay, so you've done the algebra and found the point for the line, begin (x, y) = (3, 0). Now use the derivative to find the slope at the point. Then plug this slope and the point into the point-slope form that you learned back in algebra (here), and simplify to find the equation of the tangent line.

If you get stuck, please reply showing your efforts so far. Thank you! ;)
 
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