A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve y² = 4x + 5. Then, the point of contact is

• (2, 1)

• (- 1, 1)

• (1, 3)

• (3, 4)

The function f(x) = 2x³ - 15x² + 36x + 6 is strictly decreasing in the interval

• (2, 3)

• $\left(- \infty , 2\right)$

• (3, 4)

• $\left(- \infty , 3\right) \cup \left(4, \infty \right)$

The slope of the tangent to the curve y²e^xy = 9e^{- 3}x² at (- 1, 3) is

• $\frac{- 15}{2}$

• $\frac{- 9}{2}$

• 15

• $\frac{15}{2}$

The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm, then the rate of decreasing of its height is

• 6 cm/min

• 3 cm/min

• 4 cm/min

• 5 cm/min

The slope of the normal to the curve y = x² - $\frac{1}{{\mathrm{x}}^2}$ at (- 1, 0) is

• $\frac{1}{4}$

• $- \frac{1}{4}$

• 4

• - 4

The minimum value of sin(x) + cos(x) is

• $\sqrt{2}$

• $- \sqrt{2}$

• $\frac{1}{\sqrt{2}}$

• $- \frac{1}{\sqrt{2}}$

The slope of the tangent to the curve y = 3x² - 5x + 6 at (1, 4) is

• - 2

• 1

• 0

• - 1

The chord joining the points (5, 5) and (11, 227) on the curve y = 3x² - 11x - 15 is parallel to tangent at a point on the curve. Then, the abscissa of the point is

• - 4

• 4

• - 8

• 8

The function f(x) = sin(x) - kx - c, where k and c are constants, decreases always when

• k > 1

• $\mathrm{k} \ge 1$

• k < 1

• $\mathrm{k} \le 1$

If y = mlog(x) + nx² + x has its extreme values at x = 2 and x = 1, then 2m + 10n is equal to

• - 1

• - 4

• - 2

• - 3