Plus Two Maths Chapter Wise Questions and Answers Chapter 5 Continuity and Differentiability

Plus Two Maths Continuity and Differentiability Three Mark Questions and Answers

                  

   

Plus Two Maths Continuity and Differentiability Four Mark Questions and Answers

      

                  

    

Plus Two Maths Continuity and Differentiability Six Mark Questions and Answers

Question 1.

1. Verify mean value theorem for the function f(x) = (x – 2)2 in [1, 4].
2. Find a point on the curve y = (x – 2)2 at which the tangent is parallel to the chord joining the points (1, 1) and (4, 2)
3. Find a point on the above curve at which the tangent is parallel to the x-axis.

Answer:
1. f(x) = (x – 1)2, x ∈ [1, 4]
f(x) is continuous in [1, 4]
f'(x) = 2(x – 2) is differentiable in [1, 4]
Then there exists c ∈ [1, 4] so that