Hi Guy,
Am stuck with 3 questions for some questions about application of differentiation.
Would appreciate if any kind souls can englighten me on how to do the questions thanks !
NewDocument1(2).pdf
Hi Guy,
Am stuck with 3 questions for some questions about application of differentiation.
Would appreciate if any kind souls can englighten me on how to do the questions thanks !
NewDocument1(2).pdf
For 2 of the questions, i have written down the questions here :
1) The Equation y = [bx2 +1/(1+x)(a-x)] has horizontal asymptote y = -1 and vertical asymptotes x = 1, x=-1. Deduce the value of a and b. Find the turning points of the curve y = [bx2 +1/(1+x)(a-x)] and deduce the nature of the turning point. Sketch the graph indicating clearly the essential geometrical features
2) An open tank with a square base is to be made from a thin sheet of metal. Find the length of the square base and the height of the tank so that the least amount of paint used to paint the tank with a capacity of 8cm3 ( You may assume that h is the height of the tank and x represents the side of the square base.)
Please help guys if possible.
Thanks.
Well, what have you done on this? What is the derivative of $\displaystyle y= bx^2+ \frac{1}{(1+x)(a- x)}= bx^2+ (1+x)^{-1}(a- x)^{-1}$? What is the definition of "turning point"?
What is the formula for the volume of a rectangular solid with square base of side x and height y?2) An open tank with a square base is to be made from a thin sheet of metal. Find the length of the square base and the height of the tank so that the least amount of paint used to paint the tank with a capacity of 8cm3 ( You may assume that h is the height of the tank and x represents the side of the square base.)
What is the formula for the surface area?
Can you solve the equation for volume for y and then replace y in the formula for surface area by that?
How do you find the minimum value of a function?
Please help guys if possible.
Thanks.