Page 48 - Mathematics Class - XII

Viva-Voce

1. What is secant line?
Ans. The line connecting the endpoints of graph is secant line.

2. What is tangent line?
Ans. A tangent line to the function f (x) at the point x = a is a line that just touches the graph of the function.
3. What is a continuous function?

Ans. A function is continuous over an interval, if it is continuous at each point in that interval.
4. Why is continuity necessary in Rolle’s theorem?

Ans. A discontinuous function could have tangent lines that aren’t parallel to the secant line anywhere on the
interval.
5. Why is differentiability necessary in Rolle’s theorem?
Ans. If a continuous function is not differentiable over the interval, the slope of the tangent lines are not parallel
to the slope of the secant line anywhere on the interval (the slopes of the tangent lines are constant, but not
equal to the slope of the secant line).

6. What does mean value theorem tell us?
Ans. The mean value theorem states that if a function f is continuous on the closed interval [a, b] and differentiable
on the open interval (a, b), then there exists a point c in the interval (a, b) such that f ′(c) is equal to the
function’s average rate of change over [a, b].

MCQs

1
3
2

1. If Rolle’s theorem holds for the function, f (x) = x + bx + ax + 5 on [1, 3] with c 2 , find the value
of a and b. 3
a) a = 11, b = – 6 b) a = 10, b = 6 c) a = –11, b = 6 d) a = 11, b = 6
2. The value of c in Rolle’s theorem for the function f (x) = e sin x, x ∈ [0, π] is
x
p p p
a) b) c) d)
6 4 2 4

3. The value of c in Rolle’s theorem for the function, f (x) = sin 2x in 0, 2 is

p p p p
a) b) c) d)
2 3 4 6

p
Answers: 1. a) a = 11, b = – 6 2. d) 3. c)
4 4

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