Increasing And Decreasing

[Ryan Rigdon]

I have this problem with this ? cant seem to get the increasing and decreasing part right.

the problem

Determine the intervals where the graph of the given function is increasing, decreasing, concave up and down. Then sketch the graph.

g(x) = 3x^4 - 3x^3 +1

MY WORK.

1. Find f'(x) f'(x) = 12x^3 - 9x^2
2. Set f'(x) = 0 & solve. 12x^3 - 9x^2 = 0 x^(2) (12x-9) = 0 x = 0 x = 3/4

Split points are 0, 3/4 (-infinity, 0) , (0,3/4) , (3/4,infinity)

(-infinity,0) Eval. f'(x) @ x = -1
f'(-1) = -3 y decreasing on (-infinity, 0] by Monotonicity Theorem

(0,3/4) Eval. f'(x) @ x = 1/4
f'(1/4) = 12(1/4)^3 - 9(1/4)^2 = 12(1/64) - 9(1/16) = 12/64 - 36/64 = -24/64 = -3/8
y is decreasing on [0,3/4] by Monotonicity Theorem

(3/4,infinity) Eval. f'(x) @ x = 1
f'(1) = 3 y is increasing on [3/4,infinity) by Monotonicity Theorem


What is wrong with my increasing and decreasing?

 

[Deleted member 4993]

I have this problem with this ? cant seem to get the increasing and decreasing part right.

the problem

Determine the intervals where the graph of the given function is increasing, decreasing, concave up and down. Then sketch the graph.

g(x) = 3x^4 - 3x^3 +1

MY WORK.

1. Find f'(x) f'(x) = 12x^3 - 9x^2
2. Set f'(x) = 0 & solve. 12x^3 - 9x^2 = 0 x^(2) (12x-9) = 0 x = 0 x = 3/4

Split points are 0, 3/4 (-infinity, 0) , (0,3/4) , (3/4,infinity)


(-infinity,0) Eval. f'(x) @ x = -1
f'(-1) = -3 y decreasing on (-infinity, 0] by Monotonicity Theorem

(0,3/4) Eval. f'(x) @ x = 1/4
f'(1/4) = 12(1/4)^3 - 9(1/4)^2 = 12(1/64) - 9(1/16) = 12/64 - 36/64 = -24/64 = -3/8
y is decreasing on [0,3/4] by Monotonicity Theorem

(3/4,infinity) Eval. f'(x) @ x = 1
f'(1) = 3 y is increasing on [3/4,infinity) by Monotonicity Theorem


What is wrong with my increasing and decreasing?

Did you sketch the graph?

What is happening at x=0?

You'll see the function is continuously decreasing or flat from x = -? to x = ¾

y' ? 0 in that range. So you could say function is decreasing for (-?,0)U(0,¾)

 

[Ryan Rigdon]

the only choices that are given to me are as follow

The function is decreasing on

A. (0,1/2) B. (-infinity,0) and (1/2, infinity) C. (-infinity,3/4] D. [3/4,infinity)



if i had to choose i would go with C.

 

[Deleted member 4993]

the only choices that are given to me are as follow

The function is decreasing on

A. (0,1/2) B. (-infinity,0) and (1/2, infinity) C. (-infinity,3/4] D. [3/4,infinity)



if i had to choose i would go with C.

Given the domain of choices - you are correct.

 

[Ryan Rigdon]

thank you for the help hints Subhotosh Khan

 

[BigGlenntheHeavy]

\(\displaystyle Here \ is \ the \ graph \ of \ g(x) \ = \ 3x^4-3x^3+1.\)

\(\displaystyle They \ say \ a \ picture \ is \ worth \ a \ thousands \ words, \ is \ it?\)

[attachment=0:2p5858k7]ddd.jpg[/attachment:2p5858k7]

 

[Ryan Rigdon]

got the same graph on my calculator.