Question

Consider the figure given below

Here, graph of a continuous function defined on a closed interval $[a, d]$.
Based on above information which of the following is correct?

• A. The function $f$ has a local minimum value as $f(b)$ and local maximum value as $f(c)$
• B. $f$ has absolute maximum value $f(a)$ and absolute minimum value $f(d)$
• C. Both (a) and (b) are correct
• D. Both (a) and (b) are incorrect

Answer 1

Answer: (C)

The given graph of a continuous function is defined on a closed interval $[a, d]$. We see that the function $f$ has a local minima at $x=b$ and local minimum value as $f(b)$. The function also has a local maxima at $x=c$ and local maximum value is $f(c)$.

Also, from the graph, it is evident that $f$ has absolute maximum value $f(a)$ and absolute minimum value $f(d)$. Further note that the absolute maximum (minimum) value of $f$ is different from local maximum (minimum) value of $f$.