Quadratic EquationHard
Question
The greatest value of the function $f(x) = x^{4} - 6bx^{2} + b^{2}$ on the interval $\lbrack - 2,1\rbrack$ depending on the parameter $b$ is
Options
A.$b^{2}$ if $b \geq \frac{2}{3}$
B.$16 - 24\text{ }b + b^{2}$ if $b \leq \frac{2}{3}$
C.$4 - 12b + b^{2}$ if $0 \leq b \leq \frac{4}{3}$
D.$16 - 24\text{ }b + b^{2}$ if $b \geq \frac{2}{3}$
Solution
$f(t) = t^{2} - 6bt + b^{2},\ t \in \lbrack 0,4\rbrack$
maximum value of $f(t)$
$$= \left\{ \begin{matrix} f(4) = 16 - 24b + b^{2}, & 3b \leq 2 \\ f(\rho) = b^{2}, & b \geq 2 \end{matrix} \right.\ $$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
The factors of 2x2 − x + p are rational if -...If $\alpha$ and $\beta(\alpha < \beta)$ are the roots of the equation $( - 2 + \sqrt{3})(|\sqrt{x} - 3|) + (x - 6\sqr...The equation $(x - a)(x - a - b) = 1$, where $a,b$ are positive constants has...Sum of roots is −1 and sum of their reciprocals is , then equation is -...If x − 2 is a common factor of x2 + ax + b and x2 + cx + d, then -...