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12th Standard English Medium Maths Subject Application of Differential Calculus Book Back 2 Mark Questions with Solution Part - I

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 10

    2 Marks

    5 x 2 = 10
  1. Find the slope of the tangent to the curves at the respective given points.
    x = a cos3 t, y = b sin3 t at t = \(\frac { \pi }{ 2 } \)

  2. Find the point on the curve y = x2 − 5x + 4 at which the tangent is parallel to the line 3x + y = 7.

  3. A truck travels on a toll road with a speed limit of 80 km/hr. The truck completes a 164 km journey in 2 hours. At the end of the toll road the trucker is issued with a speed violation ticket. Justify this using the Mean Value Theorem.

  4. Suppose f(x) is a differentiable function for all x with f'(x) ≤ 29 and f(2) = 17. What is the maximum value of f(7)?

  5. Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.
    \(f(x)=|\frac{1}{x}|, x\in [-1,1]\)

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