(a) State the criterion that links the sign of the first derivative with the…
MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
(a) State the criterion that links the sign of the first derivative f′(x) with the monotonic behaviour of a differentiable function f(x) on an interval.
(b) For f(x)=x3−3x+3, the first derivative is f′(x)=3x2−3. Create a sign chart of f′(x), clearly indicating the intervals on which f′(x) is positive, negative, or zero.
(c) Using your result in part (b), explain why f(x) attains a local maximum at one critical point and a local minimum at the other. Give the coordinates of both points of local extremum.