## Related questions with answers

Question

Let f be a constant function-that is, let f(x)=c, where c is some real number. Show that every number a gives rise to an absolute maximum and, at the same time, an absolute minimum of f.

Solution

VerifiedStep 1

1 of 2Since $f$ is a constant function such that $f(x) = c$, we have

$f'(x) = 0\ \ \ \text{for all}\ x$

Therefore, for every number $a$ in any closed interval $[p,q]$

$f'(a) = 0$

and so, every number $a$ will give an absolute maxima and at the same time, an absolute minima of $f$ which will be equal to

$f(a) = c$

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