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Find the absolut maximum and absolute minimum values of the function f(x)= 4x/8x+4

On the interval [3,7]

I'm quite lost on this question, if someone can work through it completely so i have a worked example for further question sit would be appreciated. Thanks

user142105
  • 21

1 Answers1

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Using the equality $$\left(\frac fg\right)'=\frac{f'g-g'f}{g^2}$$ we find that $$f'(x)=\frac{4(8x+4)-8(4x)}{(8x+4)^2}=\frac{16}{(8x+4)^2}>0$$ hence $f$ is strictly increasing on the interval $[3,7]$ and then $$\min f=f(3)=\frac{3}{7}\quad\text{and}\quad \max f=f(7)=\frac7{15}$$