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f (x) is cubic polynomial which has local maximum at x = 1, f (b) = 18, f (a) = 1 and f’ (x) has local maximum at x = 1. If f (b) = 18, f (a) = 1 and f’ (x) has local minimum at x = 0, then

1) The distance between (-1, 2) and (a, f (a)), where x = 0 is the point of local minima... View Article

1) for at least one x in the interval [1, ∞], f (x + 2) – f (x) < 2... View Article

1) Equation of curve is x (dy / dx) – 3y = 0 2) Normal at (1, 1) is x... View Article

1) 3√2 / 8 2) 2√3 / 8 3) 3√2 / 5 4) √3 / 4 Solution: (1) 3√2 /... View Article

1) √37 km/h 2) 37 km/h 3) 13 km/h 4) √13 km/h Solution: (1) √37 km/h The speed of x... View Article

1) 1 / 243 2) 1 / 27 3) -5 4) 1 / 5 Solution: (1) 1 / 243 y... View Article

Solution: f (x) = eg(x) eg(x+1) = f (x + 1) = x f (x) = xeg(x) and g (x... View Article

1) -2 2) -1 3) 0 4) 1 / 2 Solution: (4) 1 / 2 For Rolle’s theorem to be... View Article

1) 35 / 16 2) 35 / 48 3) 7 / 6 4) 5 / 16 Solution: (2) 35 /... View Article

1) f (x) = {(1 / 2) – x, when x < 1 / 2 and [(1 / 2) –... View Article

1) 0.05% 2) 0.0025% 3) 0.25% 4) 0.1% 5) 0.2% Solution: (4) 0.1% Assume the radius of the circle to... View Article

1) 0 < x < π / 8 2) π / 4 < x < 3π / 8 3) 3π... View Article

1) Increasing on [0, ∞] 2) Decreasing on (0, ∞) 3) Decreasing on [0, π / e) and increasing on... View Article

1) 3 2) 1 3) 2 4) 1 / 2 Solution: (3) 2 f (x) = 2x3 – 9ax2 +... View Article

1) e2 2) e(2-√3) 3) e4 4) 1 Solution: (3) e4 Let y = e(2+√3 cosx + sinx) y’ =... View Article

1) (a, 0) 2) (-a, 0) 3) (a / 2, √3 / 2 a) 4) (0, a) 5) (0, a2)... View Article

1) 0 2) 1 / 2 3) 1 / 3 4) 1 / 4 Solution: (4) 1 / 4 f... View Article

1) α / β 2) β / α 3) √α / β 4) √β / α Solution: (3) √α /... View Article

1) No real value of b and c 2) 0 < c < b√2 3) |c| < |b| √2 4)... View Article

1) Maxima when n = –2, –4, –6,… 2) Maxima when n = –1, –3, –5,… 3) Minima when n... View Article