Let . (i) Find and determine all stationary points of . (ii) Evaluate at each…
MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let g(x)=x4−3x3.
(i) Find g′(x) and determine all stationary points of g.
(ii) Evaluate g′′(x) at each stationary point and comment on the conclusions that might (or might not) be drawn directly from these values.
(iii) Construct a complete sign chart for g′(x) on the real line and use it to classify each stationary point as a local maximum, local minimum, or point of inflexion/saddle point.
(iv) Draw a rough sketch of the graph of g in the neighbourhood of each stationary point, clearly indicating their nature.