Question

Using Rolle’s theorem, find the point on the curve y = x(x – 4), x ∈ [0, 4], where the tangent is parallel to x-axis

Answer 1

We have, y = x(x – 4), x ∈ [0, 4]

Since given function is polynomial it is continuous and differentiable.

Also y(0) = y(4) = 0

So, conditions of Role's theorem are satisfied.

Hence there exists a point c ∈ (0, 4) such that f'(c) = 0

⇒ 2c – 4 = 0

⇒ c = 2

⇒ x = 2 and y(2)

= 2(2 – 4)

= –4

Therefore, the required point on the curve, where the tangent drawn is parallel to the x-axis is (2, – 4).