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

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 Multiple Choice QuestionsMultiple Choice Questions

271.

The slope of the tangent to the curve x = t2 + 3t - 8, y = 2t2 - 2t - 5 at the point (2, - 1) is

  • 227

  • 67

  • 76

  • - 67


272.

The equation of the normal to the curve y(1 + x2) = 2 - x, where the tangent crosses X-axis, is

  • 5x - y - 10 = 0

  • x - 5y - 10 = 0

  • 5x + y + 10 = 0

  • x + 5y + 10 = 0


273.

The maximum value of 1xx is

  • e

  • ee

  • e1/e

  • 1ee


274.

The rate of change of area of a circle with  respect to its radius at r = 2 cm is

  • 4

  • 2π

  • 2

  • 4π


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275.

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

  • (- , - 1)

  • [- 1, )

  • (- , 1]

  • (- 1, )


B.

[- 1, )

We have,       fx = x2 + 2x - 5 f'x = 2x + 2            = 2x + 1         f'x  0 2x + 1  0     x + 1  0            x  - 1

 f(x) is increasing on [- 1, ).


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276.

The point on the curve y2 = x where the tangent makes an angle of π/4 with X-axis is

  • (4, 2)

  • 12, 14

  • 14, 12

  • (1, 1)


277.

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


278.

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

  • cut at right angle

  • touch each other

  • cut at an angle π3

  • cut at an angle π4


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279.

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

  • 1, 

  • - 1, 

  • - , 

  • 0, 


280.

For all real values of x, increasing function is

  • x- 1

  • x2

  • x3

  • x4


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