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Course: MAT421 Calculus I

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QUESTION 3 a) b) The volume ofan open cylindrical tank is 100 n1a . Given that r is the radius of the circular base and h is the height of the tank. i) Show that the total surface area of the tank is given by A = m2 +@. f ii) Find the value of r and h that will minimize the total surface area ofthe tank. (8 marks) Consider a function {(x) = x3 + g 2x + 5. i) Find the intervalfs} where the function f (X) is increasing or decreasing. ii) Find the interva|(s) where the function f(x} is concave upward or downward. (8 marks) The MeanValue Theorem for differentiation states that if f (x) is differentiable an {ab} and continuous on [ab], then there is at least one point c in (ab) where m): rimat ba If x}: x+2, nd the exact value of c in the interval (1,2) that satises the above theorem. (4 marks)