1. **State the problem:** We are given the function $f(t) = t^4 - 4t^2 + 11$ and want to analyze or simplify it. 2. **Formula and rules:** This is a polynomial function. We can try to factor it or find its critical points by taking derivatives. 3. **Rewrite the function:** Notice it is a quartic polynomial with only even powers of $t$. 4. **Try substitution:** Let $x = t^2$, then $f(t) = x^2 - 4x + 11$. 5. **Complete the square:** $$x^2 - 4x + 11 = (x^2 - 4x + 4) + 7 = (x - 2)^2 + 7$$ 6. **Back-substitute:** $$f(t) = (t^2 - 2)^2 + 7$$ 7. **Interpretation:** Since $(t^2 - 2)^2 \geq 0$, the minimum value of $f(t)$ is $7$ when $t^2 = 2$, i.e., $t = \pm \sqrt{2}$. **Final answer:** $$f(t) = (t^2 - 2)^2 + 7$$ Minimum value is $7$ at $t = \pm \sqrt{2}$.