Question

The figure shows the graph of a function f. Which of the following has the greatest value ?

• A. $f\left(a\right)$
• B. $f\left(b\right)$
• C. $f\left(c\right)$
• D. $f\left(d\right)$

Answer 1

Answer: (C)

$f\left(c\right)$

We know that, A function $f\left(x\right)$ posses maxima at any point $x$ if $f^{\prime }\left(x\right)=0$
i.e. tangent is parallel to x-axis.
It is clear from graph that $f^{\prime }\left(c\right)=0$, also the graph's nature is concave downward i.e. $f^{\prime \prime }\left(x\right)<0$
Hence $f\left(c\right)$ is the maximum vale of the given function.