Question

If $14$ is the maximum of $-\lambda x^2+\lambda x+8$, then the value of $\lambda$ is

• A. $24$
• B. $\sqrt[6]{63}$
• C. $\sqrt[-6]{-63}$
• D. $-12$

Answer 1

The correct option is A $24$

$-\lambda x^2+\lambda x+8$

$=-\lambda (x^2-x-\frac{8}{\lambda })$

$=-\lambda \left((x-\frac{1}{2}{)}^2-\frac{1}{4}-\frac{8}{\lambda })\right)$

$=-\lambda (x-\frac{1}{2}{)}^2)+\frac{\lambda }{4}+8$

Maximum value of the expression is: $8+\frac{\lambda }{4}$

$8+\frac{\lambda }{4}=14$

$\lambda =24$