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Problem 55

$53-56$ (a) Use a graph to estimate the absolute…


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Problem 54

(a) Use a graph to estimate the absolute maximum and
minimum values of the function to two decimal places.
(b) Use calculus to find the exact maximum and minimum
$$f(x)=e^{x}+e^{-2 x}, \quad 0 \leqslant x \leqslant 1$$


The absolute minimum value of $f(x)$ is $\approx 1.89$
The absolute maximum value of $f(x)$ is $\approx 2.85$
B.Absolute minimum value is $2^{1 / 3}+2^{1 / 3}(\approx 1.8899]$ which occurs at $x=\frac{1}{3} \ln 2$
Absolute maximum value is $e+e^{-2}[\approx 2.8536]$ which occurs at $x=1$


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