Q. 114.5( 2 Votes )

The length x of a

Answer :

Given: , and x = 8 cm and y = 6 cm


(a) Perimeter of rectangle


We know that perimeter of rectangle = 2 (l + b)


= 2 (x + y)


Differentiating both sides w. r. to t, we get



= 2 (-5 + 4)


= -2 cm/min


Perimeter of rectangle is decreasing at the rate of 2 cm/min.


(b) Area of rectangle


We know that area of rectangle = lb


= xy


Differentiating both sides w. r. to t, we get



= 8 (4) + 6 (-5)


= 32 – 30


= 2 cm2/min


Area of rectangle is increasing at the rate of 2 cm2/min.


OR


Given: f (x) = sin x + cos x, 0 ≤ x ≤ 2π


f’ (x) = cos x – sin x


We know that for stationary points, f’ (x) = 0


cos x – sin x = 0


tan x =1


x = π/4, 5π/4 as 0 ≤ x ≤ 2π


The points x = π/4 and x = 5π/4 divide the interval [0, 2π] into following disjoint intervals: (0, π/4), (π/4, 5π/4) and (5π/4, 2π)



Here f is strictly increasing in the intervals (0, π/4) and (5π/4, 2π) and f is strictly decreasing in the interval (π/4, 5π/4).


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find which of theMathematics - Exemplar

Discuss the contiRD Sharma - Volume 1

Find which of theMathematics - Exemplar

Find which of theMathematics - Exemplar

If <iMathematics - Exemplar

<img width=Mathematics - Exemplar

Find the value ofMathematics - Exemplar

Discuss the contiRD Sharma - Volume 1

Discuss the contiRD Sharma - Volume 1

Find the value ofMathematics - Exemplar