adsense
How many integer values of the parameter \(m\) so that the function \(y = – {x^4} + 6{x^2} + mx\) have three extreme points?
A. \(17\).
B. \(15\).
C. \(3\).
D. \(7\).
The answer:
Select REMOVE
We have: \(y’ = – 4{x^3} + 12x + m\). Consider the equation \(y’ = 0 \Leftrightarrow – 4{x^3} + 12x + m = 0\,\,\,\,\,\,\left( 1 \right)\).
adsense
For the function to have three extreme points, the equation \(\left( 1 \right)\) must have 3 distinct solutions.
We have: \(\left( 1 \right) \Leftrightarrow m = 4{x^3} – 12x\).
Consider the function \(g\left( x \right) = 4{x^3} – 12x\) Have \(g’\left( x \right) = 12{x^2} – 12\). Give \(g’\left( x \right) = 0 \Leftrightarrow 12{x^2} – 12 = 0 \Leftrightarrow x = \pm 1\).
Variation table of \(g\left( x \right)\)
