1. (a) For the function f(x) = 2x -4x +2 find the (i) critical values of...

 

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1. (a) For the function f(x) = 2x -4x² +2 find the (i) critical values of f(x), (ii) intervals where f(x) is increasing and decreasing (iii) local maxima and local minima of f(x). (b) Find the maximum and minimum values of 1+2sin x +3cos' x, 0<Isa/2 using 2nd derivative test. 2. (a) A rectangular enclosure is to be constructed with area 600 ft. Three sides are to be made of wood cost $7/ ft and the fourth side is to be made of cement block costing $14/ ft. What dimensions will minimize the cost? (b) Differentiate y=xsin 'x with respect to In x. dy of the following: dx 3. (a) Find 1) y = hx + Vx* ta*, (iii) x = sin? 0, y= tan 0 Inx (ii) y = x* %3D (b) Find the limits of the following: (ii) Lt e -1) tan?t t3 1/1 tan t (i) Lt 1. (a) For the function f(x) = 2x -4x² +2 find the (i) critical values of f(x), (ii) intervals where f(x) is increasing and decreasing (iii) local maxima and local minima of f(x). (b) Find the maximum and minimum values of 1+2sin x +3cos' x, 0<Isa/2 using 2nd derivative test. 2. (a) A rectangular enclosure is to be constructed with area 600 ft. Three sides are to be made of wood cost $7/ ft and the fourth side is to be made of cement block costing $14/ ft. What dimensions will minimize the cost? (b) Differentiate y=xsin 'x with respect to In x. dy of the following: dx 3. (a) Find 1) y = hx + Vx* ta*, (iii) x = sin? 0, y= tan 0 Inx (ii) y = x* %3D (b) Find the limits of the following: (ii) Lt e -1) tan?t t3 1/1 tan t (i) Lt

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