Sketch the graph y = (x + 3x 5)(2x 3). Provide all working for finding the...

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Sketch the graph y = (x + 3x 5)(2x 3). Provide all working for finding the x- and y- intercepts. Find the derivative dy/dx. We did not learn how to factorise cubics in this unit so here is some information for you to use to find the stationary points. There are two stationary points. The x-values of these two points are in the set {-2,-1,21,0, 1, 1,2}. Use either the second derivative test or a sign test with sign diagram to classifying these stationary points. TASK 2: A manufacturer needs a metal tank to hold 1331 m of paint. It is to have a circular base and to be open at the top. The side of the tank is to be made by a rectangle of steel 'rolled around' to form a cylinder that has the same circumference as the base. Find the dimensions that minimise the materials required to make the tank, and so reduce the cost of making the tank. (1) What is the area and circumference of a circle? (2) What is the volume of a cylinder? (3) Use the answers in (1) and (2) to find the function for the area of metal required to make the tank. (The total area for the metal base and rectangle used for the side only). (4) Use calculus to find the dimensions (radius and height) that minimise the metal used. Show all working. (5) Demonstrate that these dimensions do minimise (and don't maximise) the metal used. Show all working. Sketch the graph y = (x + 3x 5)(2x 3). Provide all working for finding the x- and y- intercepts. Find the derivative dy/dx. We did not learn how to factorise cubics in this unit so here is some information for you to use to find the stationary points. There are two stationary points. The x-values of these two points are in the set {-2,-1,21,0, 1, 1,2}. Use either the second derivative test or a sign test with sign diagram to classifying these stationary points. TASK 2: A manufacturer needs a metal tank to hold 1331 m of paint. It is to have a circular base and to be open at the top. The side of the tank is to be made by a rectangle of steel 'rolled around' to form a cylinder that has the same circumference as the base. Find the dimensions that minimise the materials required to make the tank, and so reduce the cost of making the tank. (1) What is the area and circumference of a circle? (2) What is the volume of a cylinder? (3) Use the answers in (1) and (2) to find the function for the area of metal required to make the tank. (The total area for the metal base and rectangle used for the side only). (4) Use calculus to find the dimensions (radius and height) that minimise the metal used. Show all working. (5) Demonstrate that these dimensions do minimise (and don't maximise) the metal used. Show all working.