Question

f(x) = ln(10-x^2), x=[-3,3], find the point in interval [-3,3] where slope of a tangent is zero,

(a) 0

(b) Rolle’s Theorem is not applied, because function is not continuous in interval [-3,3]

(c) Rolle’s Theorem is not applied, because function is not differential in interval (-3,3)

(d) 2

This question was posed to me at a job interview.

My question is from Rolle’s Theorem in chapter Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (a) 0

To elaborate: Domain of f(x) = [-√10, +√10]

Hence given f(x) is continuous in interval [-3,3]

f’(x) = \(\frac{-2x}{10-x^2}\)

⇒ x ≠ ±√10

⇒ Domain of f’(x) = (-∞,∞)- ±√10

⇒ Hence f(x) is differential in interval (-3,3)

f’(c) = -2c/(10-c^2) = 0

⇒ c=0.