anonymous
  • anonymous
Not sure how to do this: Please explain??? :D Write down the set of values of the constant k for which the equation 2X^3-3X^2-12X-7=k has exactly one real solution. Thanksss
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
nice drawing :P
anonymous
  • anonymous
isnt it finding a value for k????
anonymous
  • anonymous
lol...tnx so for any real number \(k\) there is exactly one solution for the equation see the intersects of horizental lines and \(f(x)\)

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anonymous
  • anonymous
why do u differentiate the equation ?
anonymous
  • anonymous
|dw:1345805312784:dw|
anonymous
  • anonymous
because i want to see what is the behaviour of function
anonymous
  • anonymous
if it was something like this|dw:1345805467267:dw| for some values between \(k_1\) and \(k_2\) there is more than one real root
anonymous
  • anonymous
so i differentiate it to see if there is some critical points like last drawing or not.
anonymous
  • anonymous
so is the answer k=all real numbers?
anonymous
  • anonymous
i think yes...if im not wrong
anonymous
  • anonymous
oops : misread : \[f(x)=2x^3−3x^2−12x−7\]\[f'(x)=6x^2-6x-12=0\]it gives \(x^2-x-2=0\) so \(x=-1,2\) so we have two critical points
anonymous
  • anonymous
sorry @Snowflake123 ...
Mimi_x3
  • Mimi_x3
you sub the x back into the y for k i think..
anonymous
  • anonymous
exactly
anonymous
  • anonymous
so whats the k values
Mimi_x3
  • Mimi_x3
why not you try and sub it back in
Mimi_x3
  • Mimi_x3
sub it into y = 2x^2 - 3x^2 - 12x - 7
Mimi_x3
  • Mimi_x3
2x^3**
anonymous
  • anonymous
so the graph will be like this|dw:1345806482815:dw| just try to work it out
Mimi_x3
  • Mimi_x3
why are there two k's?
anonymous
  • anonymous
the equation \(f'(x)\) has 2 roots so there are 2 k's we must work it out
Mimi_x3
  • Mimi_x3
according to my notes dont you find the roots from the stationary points? so there is only one line \(y=k\)
anonymous
  • anonymous
for \(k=k_1,k_2\) there are exactly 2 real roots for the equation \(f(x)=k\) for \(k_1
anonymous
  • anonymous
so the region we lookin for is \[k>k_2 \ \text{&} \ k
anonymous
  • anonymous
what do u mean by '' there is only one line y=k''
Mimi_x3
  • Mimi_x3
woops forget it i made a mistake; youre right
anonymous
  • anonymous
lol...i hope im right...
Mimi_x3
  • Mimi_x3
yes you are!! i just drew abit it differently so got kinda confused

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