Question

for the curve with the equation y = 3x^2 -x^3, find the values of x for which y is decreasing

Answer 1

Learn the standard form for a quadratic equation. The equation is y = ax^2 + bx + c. The letters a, b and c represent coefficients.
Determine whether the value of the a coefficient of your equation is equal to zero. For example, your equation is y = 7x + 11. The "a" coefficient is equal to 0: y = 0x^2 + 7x + 11. Your equation represents a line.
determine whether the value of the "a" coefficient of your equation is not equal to zero. For example, your equation is y = 3x^2 + 7x + 11. The "a" coefficient is not equal to 0; it is equal to 3.

Answer 2

ummm my question is y = 3x^2 -x^3
which can be written as y =-x^3 + 3x^2

Answer 3

i don't understand why what you just wrote has anything to do with solving the question , other than telling me about basic quadratic functions

Answer 4

y'=6x-3x^2
-3x^2+6x=0
-3x(x-2)=0
x=0, 2
divide the domain into 3 intervals
(-infinity, 0), (0, 2), and (2, infinity)
test a sample from each domain and find the sign of the test. if the sign is negative, its decreasing

Answer 5

from each interval*

Answer 6

ya in simpler lang. @dock... is correct

Answer 7

no rohangrr, you were completely off, but thanks for trying. i'll give you are medal anyways

Answer 8

DOCKWORKER can i just use 2nd derivative to test instead of split it into 3 intervals?

Answer 9

sure, but its quite easy using 1st derivative test in this case

Answer 10

oh i see, so if i did use second derivative when i test it for x=0, second derivative is 6 which is > 0
but for x=2, second derivative is -6 which is <0
hence y is decreasing at x =2
is this how i would do it dockland?

Answer 11

oh sorry i mean dockworker not dockland. my apologies!

Answer 12

2nd derivative test would tell you if there was a max or min at that point, not if it was increasing or decreasing

Answer 13

oh i see, so could you show me how i would do it using second derivative please?

Answer 14

y''=-6x+6
-6(0)+6=6, so f(0) is a local minimum
-6(2)+6=-6, so f(6) is a local max
for x=0 to produce a min, the graph would switch from decreasing before x=0 to increasing after x=0.
for x=2 to produce a max, the graph would be increasing before x=2 to increasing after x=2

Answer 15

so its decreasing on the interval [-infinity, 0)U(2, infinity)

Answer 16

(-infinity, 0)U(2, infinity)**

Answer 17

oh i see! THANK YOU DOCKWORKER! your help is greatly appreciated!

Answer 18

you're welcome

Answer 19

@virtus see this photos