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(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find the local maximum and minimum values of $f .$(c) Find the intervals of concavity and the inflection points.$f(x)=e^{2 x}+e^{-x}$
A. $f(x)$ is decreasing on $\left(-\infty,-\frac{1}{3} \ln (2)\right)$ and increasing on $\left(-\frac{1}{3} \ln (2), \infty\right)$B. $\min :\left(-\frac{\ln 2}{3}, \frac{3 \sqrt[3]{2}}{2}\right)$C. concave up: $(-\infty, \infty),$ no inflection points
Calculus 1 / AB
Chapter 4
APPLICATIONS OF DIFFERENTIATION
Section 3
Derivatives and the Shapes of Graphs
Derivatives
Differentiation
Applications of the Derivative
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for this program, we can ride out the first so that the relative and the second derivative in the beginning. So for party, we want to find the increasing and decreasing interval. That means f prime because zero um so we have only one solution. X equals two minus 1/3 long off. To which means we have to consider to sub intervals from active divinity to inactive 1/3 long love too. And the front negative wanted along to three infinity over the first interval. If prime this inactive. So the pharmacy is decreasing over the second. Her life primates positive sort of function is increasing. That means we have a local Milliman at X equals two 1/3 known off to with value F because to 3/2 to the three to third in the for the concave it ease. The second figurative is always positive because both both the components are exponential function. They are no negative. So, uh, eighth is Khan cave. Pour it, um, own negative infinity to infinity. And then there's no inflection points
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