Please help to solve the Math Assignment questions as below:

1)A clothing manufacturer offers a discount on the unit price P, in euros (), off its shirts based on the number of shirts purchased, s. P'[S)=0.004S is the function that gives the rate of change in the unit price of the shirts, and 9 shirts cost 9.75each. How much would each shirt cost if a clothing retailer purchased 40 for sale in their store? 2)Consider two polynomial functions f(x] and g(x]. The constant term for f(x] is 8 and the constant term for g[X) is 2. If f'[X)=g'(X], write an expression for the difference between the integrals of these functions, if the constant of integration is the same for both functions. 3)Evaluate I[X+ 2)/ [x+1) 2dx 4)Find the area bounded by the curve y=1/9+x2, the x and y-axes, and the line X=3. Give your answer as a decimal correct to three significant gures. 5) The diagram below shows parts of the curve of y 2X2 and the line y=X+12y. Find the area of the shaded region. 6) Let f \"(x)=3x22. Find f(x] if f'[1) = 0. 7) Given that f '(x)=3x2+kx, f(0)=9 and f(2)=1, find the value of k 8) sine: Find the area enclosed by the curve of f(x) = , :r: 75 O, the m-axis, and the a: vertical lines a: = l and a: = 3. Give your answer correct to 3 signicant gures. Do not include units in your answer. 9) 3 Findf dm. :32 10) Choose the integral that represents the area of the shaded region. 11) . . Find the maximum gradient of the function y = a;\" + 3::2 + 9:: 27 12) Given ax) = (:05 22:, nd f\"(a:). 13) Consider the function dened by f(x) = 3331-1 Find f\" (1). Give an exact answer. 14) The gradient of the tangent to the graph of the function f(a:) = 2:3 + 53':2 +6 is negative for which values of at? 15) Given y1= , determine the number of stationary values of y2 = I . y1 16) Part of the graph of f"(x) for a function f is given below. How many points of inflexion does f have in the given interval? 10 -2 0 2 -10 1 17) The inflexion point of the graph of f(x) = sinx - 2 cos x in the interval 0