(a) Define a stationary point of a real-valued function. (b) State the usual criteria…
MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
(a) Define a stationary point of a real-valued function.
(b) State the usual criteria of the second derivative test for identifying a local maximum or a local minimum at a stationary point.
(c) Give a brief reason why the test fails when the second derivative at the stationary point equals zero.
(d) For the function f(x)=x4,
(i) locate all stationary points,
(ii) evaluate f′′(x) at each of those points, and
(iii) determine the nature of the stationary point at x=0, justifying your answer with an argument that remains valid even though f′′(0)=0.