MrCodeDude
Lifer
QUESTION
The maximum velocity of a particle on the interval 0 < t < 4 by a particle who's position is given by s(t) = x^4 + 4x^3 - 48x^2 + 12x - 6 is:
MY ANSWER
First thing I do is derive the position equation to get velocity equation.
v(t) = 4x^3 + 12x^2 - 96x + 12
Then, I needed to find the max and mins of that equation, so I derive it once again
v'(t) = 12x^2 + 24x - 96
Divide by 12 to make equation look nice 🙂
v'(t) = 12 ( x^2 + 2x - 8)
Factor
v'(t) = 12 (x + 4)(x - 2)
So I get the numbers -4 and 2. But because the interval is from 0 to 4, I disgard -4.
So then, I take the answer of 2 and plug it back into the v(t) equation.
I get:
v(2) = 4(2)^3 + 12(2)^2 - 96(2) + 12
v(2) = 32 + 48 - 192 + 12
v(2) = -100
But, I also have to plug in end points, so:
v(0) = 4(0)^3 + 12(0)^2 - 96(0) + 12
v(0) = 12
and
v(4) = 4(4)^3 + 12(4)^2 - 96(4) + 12
v(4) = 256 + 192 - 384 + 12
v(4) = 76
Because velocity can be positive and negative, I just take the number greatest away from zero.
That number being -100. And that's my answer...
Is that correct?
The maximum velocity of a particle on the interval 0 < t < 4 by a particle who's position is given by s(t) = x^4 + 4x^3 - 48x^2 + 12x - 6 is:
MY ANSWER
First thing I do is derive the position equation to get velocity equation.
v(t) = 4x^3 + 12x^2 - 96x + 12
Then, I needed to find the max and mins of that equation, so I derive it once again
v'(t) = 12x^2 + 24x - 96
Divide by 12 to make equation look nice 🙂
v'(t) = 12 ( x^2 + 2x - 8)
Factor
v'(t) = 12 (x + 4)(x - 2)
So I get the numbers -4 and 2. But because the interval is from 0 to 4, I disgard -4.
So then, I take the answer of 2 and plug it back into the v(t) equation.
I get:
v(2) = 4(2)^3 + 12(2)^2 - 96(2) + 12
v(2) = 32 + 48 - 192 + 12
v(2) = -100
But, I also have to plug in end points, so:
v(0) = 4(0)^3 + 12(0)^2 - 96(0) + 12
v(0) = 12
and
v(4) = 4(4)^3 + 12(4)^2 - 96(4) + 12
v(4) = 256 + 192 - 384 + 12
v(4) = 76
Because velocity can be positive and negative, I just take the number greatest away from zero.
That number being -100. And that's my answer...
Is that correct?
