a) Water is running out of a conical funnel at the rate of 5 cm per...

 

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a) Water is running out of a conical funnel at the rate of 5 cm per second. The radius of the cone is 10 cm and height is 20 cm. Determine the rate of change of the water level when its level is 10 cm deep. b) Given y=2x-6x+1. Find i) the critical points ii) the maximum, minimum or saddle points (if any) by using Second Derivative Test. (7 marks) (8 marks) c) For f(x)=x-4x over the interval [-2,1], show that f(x) satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least on value ce (-2,1), such that f'(c) is equal to the slope of the line connecting (-2,f(-2)) and (1,f(1)). Find these values c guaranteed by the Mean Value Theorem. (5 marks) a) Water is running out of a conical funnel at the rate of 5 cm per second. The radius of the cone is 10 cm and height is 20 cm. Determine the rate of change of the water level when its level is 10 cm deep. b) Given y=2x-6x+1. Find i) the critical points ii) the maximum, minimum or saddle points (if any) by using Second Derivative Test. (7 marks) (8 marks) c) For f(x)=x-4x over the interval [-2,1], show that f(x) satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least on value ce (-2,1), such that f'(c) is equal to the slope of the line connecting (-2,f(-2)) and (1,f(1)). Find these values c guaranteed by the Mean Value Theorem. (5 marks)