Question

I literally need your help.

Find the coordinates of the stationary points on the graph of y=x^3-12x-12 and sketch the graph. Find the set of values of k for which the equation x^3-12x-12=k has more than one real solution.

Answer 1

@robtobey

Answer 2

stationary point means vertex

Answer 3

for the second part, for there to be more than one real solution, the discriminant must be GREATER than 0

Answer 4

so solve the discriminant andfind the value for where the discriminant is more than zero and it should be correct

Answer 5

@CrashOnce I have a difficulty in sketching a cubic graph.?

Answer 6

www.analyzemath.com/Graphing/graphing_cubic_function.html

Answer 7

some help even tho im not that good lol

Answer 8

lol , well I will check that out. Thanks for your help anyway :)

Answer 9

same as the vertex

Answer 10

ooh nvm it is not a quadratic

Answer 11

\[f y=x^3-12x-12\] take the derivative
\[y'=3x^2-12\] set it equal to zer0
\[3x^2-12=0\] and solve for\(x\)
\[3x^2-12=0\\
x^2-4=0\\x=\pm2\]

Answer 12

the first coordinate of the stationary point is \(2\) and also \(-2\)
to find the second coordinate, replace \(x\) by \(2\) and \(-2\)

Answer 13

you got that?

Answer 14

Yes, How about skteching :) ?

Answer 15

it is a cubic polynomial with leading coefficient and two stationary points
gotta look something like this

Answer 16

here is a better picture '
http://www.wolframalpha.com/input/?i=x^3-12x-12+

Answer 17

For graph http://www.wolframalpha.com/input/?i=graph++y%3Dx%5E3-12x-12

x^3-12x-12=k
take the derivative
k'=3x^2-12
3x^2-12=0
3x^2=12
x^2=4
x=±2

CBSE Subjects for Class 11 Arts - http://scoremore.beep.com/the-cbse-board-2014-08-13.htm