Calculus Consider the equation below. f(x) = e^(3x) + e^(−x)   (a) Find the intervals on which f is increasing. (Enter your answer using interval notation.) 1 Find the interval on which f is decreasing. (Enter your answer using interval notation.) 2 (b) Find the local minimum value of f. 3 (c) Find the interval on which f is concave up. (Enter your answer using interval notation.) 4

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`f(x)=e^(3x)+e^(-x) => f'(x)=3e^(3x)-e^(-x) =>f''(x)=9e^(3x)+e^(-x)`

f(x) is increasing if f'(x)>0, and decreasing if f'(x)<0.

`f'(x)<0=>3e^(3x)-e^(-x)<0=>`

`3e^(3x)<e^(-x)=>3e^(3x)<1/e^x=>`

(The entire section contains 141 words.)

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