The maximum value of the function f(x) = 3x3 -- 18x2 + 27x -- 40 on the set S = [ x, R:x^2…

Question

The maximum value of the function f(x) = 3x3 -- 18x2  + 27x -- 40 on the set S = $$\left\{ {x\, \in R:{x^2} + 30 \le 11x} \right\}$$ is :

Accepted Answer

S = {x $$ \in $$ R, x2 + 30 - 11x $$ \le $$ 0}

= {x $$ \in $$ R, 5 $$ \le $$ x $$ \le $$ 6}

Now f(x) = 3x3 - 18x2 + 27x - 40

$$ \Rightarrow $$  f '(x) = 9(x - 1)(x - 3),

which is positive in [5, 6]

$$ \Rightarrow $$  f(x) increasing in [5, 6]

Hence maximum value = f(6) = 122

Solutions · 1