Consider the equation below. Consider the equation below. f(x)= e^(5x) + e^(−x) Find the intervals on which f is increasing. (Enter your answer using interval notation.). Find the interval on which f
Consider the equation below.
Consider the equation below.
f(x)= e^(5x) + e^(−x)
Find the intervals on which f is increasing. (Enter your answer using interval notation.). Find the interval on which f is decreasing. (Enter your answer using interval notation.)
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You need to use derivative of the function to check its monotony such that:
`f'(x)>0=> f(x) ` increases
`f'(x)<0 => f(x) ` decreases
Hence, you need to find derivative of the given function, using the chain rule, such that:
`f'(x) = (e^(5x) + e^(−x))' => f'(x) = e^(5x)*(5x)' + e^(-x)*(-x)'`
`f'(x) = 5e^(5x) - e^(-x)`
You need to use negative power...
(The entire section contains 222 words.)
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