Question

For what value of K will ax^3 - 24x+b = k have three different roots?

Answer 1

I am not sure if I should include the a and b values.

Answer 2

I understand what you did, Also I will mention a = 2 and b = 15. I have the answer aswell, I just have no clue where they got it, so it is useless to me...

Answer 3

post the original problem, please. Sometimes, the Asker just post the part he/she stuck, that fact makes the helpers give out the wrong answer and waste time of both.

Answer 4

The curve y = ax^3 - 24x + b has a locale minimum at (2;-17)

9.1) Calculate the values of a and b
9.2) The co-ordinate of the other turning point , E , on the curve
9.3) For what value of k wil ax^3 - 24x + b = k have three different roots.
9.4) Determine the co-ordinate of the inflection point of the curve

Answer 5

9.5) for what value(s) of x will the graph f'(x) have a minimum value.

Answer 6

OMG, you take first derivative to get the critical point, then plug it into the original function to get the value of a, and b.
TOTALLY DIFFERENT PROBLEM!!!!

Answer 7

Yes, I know how to do 9.1 and 9.2 and 9.4 and 9.5/... I need help with 9.3

Answer 8

I just posted the complete question like you asked.

Answer 9

i don't understand why you stuck. from 9.1 you have a, b , just plug it into the original function to get the new function like 3x^3 +24x - 6.... = k for example. ( not those number, just example ) and solve for k .

Answer 10

as I guided you, you have a, and b already, so when k = -b you have the function has 3 roots, so ?

Answer 11

The answer given in my book says that \[k \in (-17;47)\]

Answer 12

I want to know how they got that answer

Answer 13

ok, let me check, not promise that I can give you an acceptable answer, but who knows? cross the fingers.

Answer 14

how can you have a = 2 b =15?

Answer 15

take first function " ax^3 -24x + b " and plug in the point (2; -17) that gives 1 eqaution. Then you take the derivative of the ax^3 -24x + b and insert the x point 2 and you get a = 2

Answer 16

would you please close this post and post a new one with the original problem?