Let f : ( − ∞ , ∞ ) → ( − ∞ , ∞ ) be defined by f ( x ) = x 3 + 1 Statement 1: The function fhas a local extremum at x = 0 Statement 2: The function f is continuous and differentiable on ( − ∞ , ∞ ) a

Question

Let f : ( − ∞ , ∞ ) → ( − ∞ , ∞ ) be defined by f ( x ) = x 3 + 1 Statement 1: The function fhas a local extremum at x = 0 Statement 2: The function f is continuous and differentiable on ( − ∞ , ∞ ) and f ′ ( 0 ) = 0

TestHub · Accepted Answer

Let f : ( − ∞ , ∞ ) → ( − ∞ , ∞ ) be defined by f ( x ) = x 3 + 1 . Clearly, f ( x ) is symmetric along y = 1 and it has neither maxima nor minima. ∴ Statement - 1 is false.

Mathematics - Application of Derivative Question with Solution | TestHub

Options:

Doubts & Discussion