Application of Differentiation - Maximum/Minimum & Rate of Change

A closed box with a square base of length x and height h, is to have a volume, F, of 150m^3. The material for the top and bottom of the box costs $2 per square metre, and the material for the sides of the box costs $1.50 per square metre. Fnd the value of x and h, correct to 3 decimal places, if the total cost of the materials, C is to be a minimum.
A viscous liquid is poured onto a flat surface. It forms a circular patch which grows at a steady rate of 6cm^2/s. Find,
a) the radius r, in pie, of the patch 24 seconds after pouring has commenced.
b) the rate of increase of the radius at this instant, correct to 2 decimal places.

Done reading the qns? Do and see if your answers are correct!


Click on image for enlarged view.

Related Post

A-Maths Differentiation: Finding Gradient of Curve I'm very excited to be working on the revised copy for the GCE O-Level Additional & Elementary Mathematics Ten Years Series (2003-2012) by FBP Pub...
A-Maths: Differentiation Basics 101 In this video, I discuss about the basics of how to differentiate constant, x term and x^2 term. Length of video: 4 minutes. Click here for dir...
Integration Mixed With Differentiation In Integration, unlike Differentiation, there isn't any product rule nor quotient rule. Having said this, examiners always like to present question in...
A-Math: Type of Stationary Point through First Derivative Photo Credit: mysza831 One of the applications of Differentiation is to determine the type of stationary point. This application is common in max...
Protected: Differentiation & Integration Solutions (For workshop participants only) Dear participants, Here are the solutions for questions which you are to work on your own. Click on the link to view them. If anyone can't view ...

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

3 Responses to Application of Differentiation - Maximum/Minimum & Rate of Change

  1. i came across this qu that day, and i really want to clarify if the method i used is correct or not.

    int(tan^2x - x^3)

    i changed it to int(sec^2x - 1 - x^3) instead, cos i don't think we can integrate tan.

    is that feasible?


  2. For Qn2,

    Total Cost, C =4x^2 + 6xh,

    Shouldn't it be C =4x^2 + 4xh instead?

    Maybe the question could also add in the total cost for the box


  3. The material for the top and bottom of the box costs $2 per square metre, and the material for the sides of the box costs $1.50 per square metre

    ==> Total cost for top & bottom of box = 2*2x^2 =4x^2
    ==> Total cost for sides of box = 1.5*4xh =6xh
    ==> Total cost = 4x^2 + 6xh


Leave a reply