The function f(x) = x² + 2x - 5 is strictly increasing in the interval

• $(- \infty , - 1)$

• $[- 1, \infty )$

• $(- \infty , 1]$

• $(- 1, \infty )$

The point on the curve y² = x where the tangent makes an angle of $\mathrm{\pi }$/4 with X-axis is

• (4, 2)

• $\left(\frac{1}{2}, \frac{1}{4}\right)$

• $\left(\frac{1}{4}, \frac{1}{2}\right)$

• (1, 1)

The rate of change ofvolume of a sphere with respect to its surface area when the radius is 4 cm is

• 4 cm³/cm²

• 6 cm³/cm²

• 2 cm³/cm²

• 8 cm³/cm²

The two curves x³ - 3xy² + 2 = 0 and 3x²y - y³ - 2 = 0

• cut at right angle

• touch each other

• cut at an angle $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

• cut at an angle $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

The function f(x) = cot^-1(x) + x, increases in the interval

• $\left(1, \infty \right)$

• $\left(- 1, \infty \right)$

• $\left(- \infty , \infty \right)$

• $\left(0, \infty \right)$

For all real values of x, increasing function is

• x^{- 1}

• x²

• x³

• x⁴

Maximum value of f(x) = sin(x) + cos(x) is

• 1

• 2

• $\frac{1}{\sqrt{2}}$

• $\sqrt{2}$

The greatest value of f(x) = (x + 1)^1/3 - (x - 1)^1/3 on [0, 1] is

• 1

• 2

• 3

• 1/3

The equation of normal to the circle 2x² + 2y² - 2 - 5y + 3 = 0 at (1, 1) is

• 2x + y = 3

• x - 2y = 3

• x + 2y = 3

• None of these

The minimum value of the function f(x) = 2x³ - 21x² + 36x - 20 is

• - 128

• - 126

• - 120

• None of these