Answer the following questions about monotonic behaviour on open and closed intervals.
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Answer the following questions about monotonic behaviour on open and closed intervals.
(a) State the definition of an increasing function on (i) an open interval (a,b) and (ii) a closed interval [a,b].
(b) Let pk(x)=x3+kx, where k is real. Explain, without detailed computation, whether the condition pk′(x)≥0 for all x∈(a,b) is sufficient to conclude that pk is increasing on [a,b]. Justify your answer briefly.
(c) Using your reasoning in part (b), comment on any additional verifications needed when determining the set of k for which pk is increasing on the closed interval [−1,2].