Q. If a function $f$ is continuous for all $x$ and if $f$ has a relative maximum at $(-1,4)$ and a relative minimum at $(3,-2)$, then which of the following statements must be true?
Application of Derivatives
Solution:
Aaodsc Because $f$ is continuous for all $x$, the intermediate value theorem implies that the graph of $f$ must intersect the $x$-axis. The graph must also intersect the $y$-axis since $f$ is defined for all $x$, in particular, at $x = 0$ As $f$ need not be differentiable.
Hence $A$, B and $C$ need not be correct.
