Question

Value of' 'c' of the mean value theorem for the function `f(x) = x(x - 2)`, when a = 0, b = 3/2, is

पर्याय

• 3/4

• 1/2

• 3/2

• 1/4

Answer 1

3/4

Explanation:

`f(x) = x(x - 2), a = 0` and `b = 3/2 ⇒ x ∈ [0, 3/2]`

`f^'(x) = x(1 - 0) + (x - 2) xx 1`

`f^'(x) = x + x - 2`

`f^'(x) = 2x - 2`

At `x` = 0 ⇒ `f(0)` = 0

At `x = 3/2` ⇒ `f(3/2) = 3/2 (3/2 - 2) = - 3/4`

According to the mean value theorem,

`f^'(c) = (f(b) - f(a))/(b - a) = (f(3/2) - f(0))/(3/2 - 0)`

`2c - 2 = - 3/4 xx 2/3 = - 1/2`

`2c = - 1/2 + 2 = 3/2`

∴ `c = 3/4`