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 $A=\left{x \mid x^{2}+20 \leq 9 x\right}$ is

(2009)

Show Answer

Solution:

  1. Given, $A=\left{x \mid x^{2}+20 \leq 9 x\right}={x \mid x \in[4,5]}$

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 $f(5)=7$.

Download Chapter Test

http://tinyurl.com/yxhc5me3

or

11



NCERT Chapter Video Solution

Dual Pane