Application of Derivatives 4 Question 66
69. The maximum value of the function $f(x)=2 x^{3}-15 x^{2}+36 x-48$ on the set $A={x \mid x^{2}+20 \leq 9 x }$ is
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Solution:
- Given, $A={x \mid x^{2}+20 \leq 9 x }={x \mid x \in[4,5]}$
Now, $\quad f^{\prime}(x)=6\left(x^{2}-5 x+6\right)$
Put $\quad f^{\prime}(x)=0 \Rightarrow x=2,3$
$$ f(2)=-20, f(3)=-21, f(4)=-16, f(5)=7 $$
From graph, maximum value of $f(x)$ on set $A$ is $f(5)=7$.
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