Question

Which of the following functions has a maximum value of m, where m is a positive constant?

Answer 1

The value of m in the fourth equation does not tend to zero, hence the function that has a maximum value of m, where m is a positive constant is$f(x)=-(m+x)^2$: Option D is correct.  

For any function to have a maximum, the differential of the function must be equal to zero.

If the functions in options A and B and C are differentiated and equated to zero, the values of m in each function will tend to zero as well.

For the function $f(x)=-(m+x)^2$

$f'(x) = -2(m+x)\times 1\\f'(x)=-2(m+x)\\0 = m+x\\m = -x$

Since the value of m in the fourth equation does not tend to zero, hence the  function that has a maximum value of m, where m is a positive constant is$f(x)=-(m+x)^2$  

Learn more here: brainly.com/question/12185438