If y = f(x2 + 2) and f'(3) = 5, then dydx at x = 1 is

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 Multiple Choice QuestionsMultiple Choice Questions

131.

Let f(x) = x3 - x + p (0  x  2) where p is a constant. The value c of mean value theorem is

  • 32

  • 63

  • 33

  • 233


132.

If the function fx = x2 - k + 2x +2kx - 2 for x  22                               for x = 2 is continuous at x = 2, then k is equal to

  • - 12

  • - 1

  • 0

  • 12


133.

If xexy + ye- xysin2x, then dydx at x = 0 is

  • 2y2 - 1

  • 2y

  • y2 - y

  • y2 - 1


134.

If y = tan-12x - 11 + x - x2, then dydx at x = 1 is equal to

  • 12

  • 23

  • 1

  • 32


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135.

If f(x) = cos-12cosx + 3sinx13, then [f'(x)]2 is equal to

  • 1 + x

  • 1 + 2x

  • 2

  • 1


136.

If u = tan-11 - x2 - 1x and v = sin-1x, then dudv is equal to

  • 1 - x2

  • - 12

  • 1

  • - x


137.

If y = 11 + x + x2, then dydx is equal to

  • y2(2 + 2x)

  • - 1 + 2xy2

  • 1 + 2xy2

  • - y2(1 + 2x)


138.

If g(x) is the inverse of f(x) and f'(x) = 11 + x3, then g'(x) is equal to

  • g(x)

  • 1 + g(x)

  • 1 + {g(x)}3

  • 11 + gx3


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139.

If y = f(x2 + 2) and f'(3) = 5, then dydx at x = 1 is

  • 5

  • 25

  • 15

  • 10


D.

10

Given, y = fx2 + 2On differentiating both sides w.r.t. x, we getdydx = f'x2 + 2 × 2xPut x = 1, we getdydx = f'12 + 2 × 2 = f'3 × 2      = 5 × 2       As given f'3 = 5      = 10


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140.

Let, f(x) = x2 + bx + 7. If f'(5) = 2f'72, then the value of b is

  • 4

  • 3

  • - 4

  • - 3


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