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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 19 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 19 maths textbook solution        

Answers (1)

Answer:

              12

Hint:

For maxima or minima we must have {f}'\left ( x \right )=0

Given:

y=-x^{3}+3 x^{2}+9 x-27

Solution:  we have, y=-x^{3}+3 x^{2}+9 x-27

To find the slope we differentiate the function once

{y}'=-3x^{2}+6x+9

To find the extremum points we again differentiate at equate it to zero

{{y}'}'=-6x+6

{{y}'}'=0

-6x+6=0

x=1

Now to find whether at the critical points we find a maxima or minima, we use the second derivative test

{{{y}'}'}'=-6

{{{y}'}'}'\left ( 1 \right )=-6

{{{y}'}'}'\left ( 1 \right )< 0

Hence we find maxima at x=1  in the equation of the slope. Hence the max value of the slope is {y}'\left ( 1 \right )  which is

{y}'\left ( 1 \right )=-3+6+9

{y}'\left ( 1 \right )=12

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