The function y = 2x³ - 9x² + 12x - 6 is monotonic decreasing when

• 1 < x < 2

• x > 2

• x < 1

• None of these

Maximum slope of the curve y = - x³ + 3x² + 9x - 27 is

• 0

• 12

• 16

• 32

The points on the curve x² = 2y which are closest to the point (0, 5) are

• (2, 2), (- 2, 2)

• $\left(2\sqrt{2}, 4\right), \left(- 2\sqrt{2}, 4\right)$

• $\left(\sqrt{6}, 3\right), \left(- 6\sqrt{3}, 3\right)$

• $\left(2\sqrt{3}, 6\right), \left(- 2\sqrt{3}, 6\right)$

The point on the curve y = 2x² - 4x + 5, at which the tangent is parallel to x-axis, will be

• (1, 3)

• (- 1, 3)

• (1, - 3)

• (- 1, - 3)

The interval, inwhich the function f(x) = x²e^-x is an increasing function, will be

• $\left(- \infty , \infty \right)$

• (- 2, 0)

• $\left(2, \infty \right)$

• (0, 2)

The minimum distance from the point (4, 2) to the parabola y² = 8x is

• $\sqrt{2}$

• $2\sqrt{2}$

• 2

• $3\sqrt{2}$

A particle moves so that the space described in time t is square root of a quadratic function of t. Then,

• $\mathrm{v} \propto \left(\frac{1}{\mathrm{s}}\right)$

• $\mathrm{acceleration} \propto \frac{1}{{\mathrm{s}}^3}$

• $\mathrm{acceleration} \propto {\mathrm{s}}^3$

• None of these

298.

The points at which the tangent to the curve y = x³ + 5 is perpendicular to the line x + 3y = 2 are

• (6, 1), (- 1, 4)

• (1, 6), (1, 4)

• (6, 1), (4, - 1)

• (1, 6), (- 1, 4)

Let f(x) = a - (x - 3)^8/9, then maxima of f(x) is

• 3

• a - 3

• a

• None of these

If the total cost C(x) in rupees associated with the production of x units of an item is given by C (x) = 3x³ - 2x² + x + 100. Then, the marginal change in cost, when x = 5, is

• 200

• 225

• 206

• 226