Question

Consider the equation below. (if an answer does not exist, enter dne.) f(x) = e9x + e−x (a) find the interval on which f is increasing. (enter your answer using interval notation.)

Answer 1

We have been given that

`f(x)=e^(9x)+e^(-x)`

On differentiating we get

`f'(x)=9e^(9x)-e^(-x)`

For the function to be increasing, the first derivative must be positive

f'(x)>0

`9e^(9x)-e^(-x)>0`

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Thus, the required interval is given by

`x\in \left ( -(ln3)/(5),\infty \right )`