2nd PUC Mathematics Series 8

71. If y = ax² + b, then dy/dx at x = 2 is equal to

72. If Rolle’s theorem holds for the function f(x) = x³ + bx² + ax + 5 on [1, 3] with c = (2 + 1/√3), find the value of a and b.

73. f y = (tan x)^{sin x}, then dy/dx is equal to

74. The derivative of y = (1 – x)(2 – x) ….. (n – x) at x = 1 is equal to

75. If x^y . y^x = 16, then the value of dy/dx at (2, 2) is

76. Find all the points of local maxima and local minima of the function f(x) = (x – 1)³ (x + 1)²

77. Find the local minimum value of the function f(x) = sin⁴x + cos⁴x, 0 < x < π2

78. If y=ax−b/(x−1)(x−4) has a turning point P(2, -1), then find the value of a and b respectively.

79. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

80. If y = x³ + x² + x + 1, then y