1. **State the problem:** We are given the function $f(x) = 2x^2 - e^x$ defined on the interval $[0,1]$ and a point $x^* = 0.36$. We want to evaluate or analyze the function at this point. 2. **Recall the function:** $$f(x) = 2x^2 - e^x$$ where $e$ is the base of the natural logarithm, approximately 2.71828. 3. **Evaluate $f(x^*)$:** Substitute $x = 0.36$ into the function: $$f(0.36) = 2(0.36)^2 - e^{0.36}$$ 4. **Calculate each term:** $$2(0.36)^2 = 2 \times 0.1296 = 0.2592$$ $$e^{0.36} \approx 1.4333$$ 5. **Combine the terms:** $$f(0.36) = 0.2592 - 1.4333 = -1.1741$$ 6. **Interpretation:** The function value at $x=0.36$ is approximately $-1.1741$. This completes the evaluation of $f(x)$ at the given point $x^* = 0.36$.