1. The problem asks to determine whether certain points given are local minima or maxima of the function 2. The function is $f(x) = \frac{e^{2x+1}}{e^x}$. Simplify the function first: $$ f(x) = e^{2x+1 - x} = e^{x+1} $$ 3. Since $f(x) = e^{x+1}$, it is an exponential function which is always increasing because the base $e$ is greater than 1. 4. The derivative is: $$ f'(x) = e^{x+1} $$ 5. The second derivative is: $$ f''(x) = e^{x+1} $$ 6. Since $f'(x) > 0$ for all $x$, the function is strictly increasing and has no local maxima or minima. 7. Now check the points given: (a) $(0, 2)$: Calculate $f(0) = e^{0+1} = e$. Since $e \approx 2.718 \neq 2$, this point is not on the curve and cannot be an extremum. (c) $(1, e + 1/e)$: Calculate $f(1) = e^{1+1} = e^2 \approx 7.389$. Meanwhile, $e + 1/e \approx 2.718 + 0.368 = 3.086$, which is not equal to $f(1)$, so this point is not on the curve either. 8. Since neither of the points lies on the graph and the function is strictly increasing with no local extrema, none of the options (a), (b), (c), or (d) represent local minima or maxima. **Final answer:** None of the points given is a local minimum or maximum of the function.