Question-166143

Question Number 166143 by Tawa11 last updated on 13/Feb/22

Answered by som(math1967) last updated on 14/Feb/22

y = {(2 - \sqrt{x})}^{4}

\frac{d y}{d x} = - 4 {(2 - \sqrt{x})}^{3} \times \frac{1}{2 \sqrt{x}} = - \frac{2 {(2 - \sqrt{x})}^{3}}{\sqrt{x}}

{[\frac{d y}{d x}]}_{(1, 1)} = \frac{2 {(2 - 1)}^{3}}{1} = - 2

s l o p e o f n o r m a l t h r o u g h P

= \frac{1}{2}

{[\frac{d y}{d x}]}_{(9, 1)} = - \frac{2 {(2 - 3)}^{3}}{3} = \frac{2}{3}

s l o p e o f n o r m a l t h r o u g h Q = - \frac{3}{2}

e q u n . o f n o r m a l t h r o u g h P

y - 1 = \frac{1}{2} (x - 1)

\Rightarrow x - 2 y = - 1

e q u n . o f n o r m a l t h r o u g h Q

y - 1 = - \frac{3}{2} (x - 9)

\Rightarrow 3 x + 2 y = 29

b y s o l v i n g x = 7, y = 4

R (7, 4)

A r e a o f △ P Q R = \frac{1}{2} ∣ 1 (1 - 4) + 9 (4 - 1)

+ 7 (1 - 1) ∣

= \frac{1}{2} \times 24 = 12 s q u n i t

Commented by Tawa11 last updated on 14/Feb/22

God bless you sir . I appreciate .

Commented by som(math1967) last updated on 14/Feb/22

t h a n k s f o r c o r r e c t i o n

Commented by cortano1 last updated on 14/Feb/22

\frac{dy}{dx} = 4 {(2 - \sqrt{x})}^{3} \times (- \frac{1}{2 \sqrt{x}})