1. **State the problem:** We are given the function $f(x) = 9x^2 - 4$ and need to find the value of $f(4) - f(1)$. 2. **Recall the formula:** The function is defined as $f(x) = 9x^2 - 4$. 3. **Calculate $f(4)$:** $$f(4) = 9(4)^2 - 4 = 9 \times 16 - 4 = 144 - 4 = 140$$ 4. **Calculate $f(1)$:** $$f(1) = 9(1)^2 - 4 = 9 \times 1 - 4 = 9 - 4 = 5$$ 5. **Find $f(4) - f(1)$:** $$f(4) - f(1) = 140 - 5 = 135$$ **Final answer:** $$\boxed{135}$$