1. What do you mean by derivative of f (x) at x = a? By using the denition of derivative, nd derivative of (i) f{x) = 3x + 2 (ii) f(x) = x3, (iii) f(x) = 3x2 + 2x + 4. 2. Find Where dx (i) y: 3x '4x +'\\'F 00 y: (x2+2x}(x 3J_) (iii) y=(x2+jx+l (iv) y=(x 3x \"in2)m (v) y: (x 10x+2),)(x +555\") - 5x+2 .. \"J x3 (W) y[4x_3] (v11) yx (6x 1} (viii) y: (2x+3}\"3 3. Find increasing and decreasing of the function f(x) = x3 6x2 +37. Also nd the maximum or minimum of the function. 4. The total cost of making v vats of milk is C(v) dollars where C(v) = 4.51? + 3.21:2 0.8v 5.9. (a) Write the expression for the marginal cost of vth vat. (b) What is the marginal cost of the 65th vat? 5. Integrate (i) 2x- 2 dx (ii) X 2 dx x 4x x -5 dx (iii) 3 Vx (4x) + 7 ) 3x (iv) J dx (v) [( x-Vx) (2x2+ 9)3 dx ( vi ) [ ( x + 2 vx +2 +-)dx X X 6. Evaluate (i) [ (x2 -3x +5)dx (ii) [ 16(2x+9)'dx 20 (iii) Jo 4x +1) da 20 (iv) Jo (4x + 1)3/2 dx (v) [(2x' -1) 6x dx (vi) 10 dx .6x +1 7. The marginal cost function of a product is 6+10x-6x. Obtain the total and average cost under the assumption of fixed cost is 500. 8. Find the area of the region bounded by the functions (i) f(x) =2x+3, x= -1 to x =1 (li) 60 2x + 1 ) ? ' x = 0 to x = 2. 9. Find the area of the region bounded by the x-axis and the curve f(x) =4x -x2 +21