Let be a differentiable function on whose derivative is given by f'(x)=(x-4)(x-1)^2(x+2)
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let f be a differentiable function on R whose derivative is given by
f′(x)=(x−4)(x−1)2(x+2).
The value of f at x=1 is f(1)=3. Answer the following questions.
(i) Find all critical points of f.
(ii) Determine the sign of f′(x) in each interval determined by the critical points.
(iii) Hence state the intervals on which f is increasing and those on which it is decreasing.
(iv) Classify each critical point as a point of local maximum, local minimum or neither, giving reasons based on your sign chart.