Find the gradient of the curve y = x² + 3x at x = 2.

**The reasoning** The gradient of a curve at any point is found using **differentiation**. When you differentiate, you're finding how steep the curve is at that exact spot. Given: y = x² + 3x **Step 1:** Differentiate using the power rule (bring down the power, reduce the power by 1): - dy/dx = 2x + 3 **Step 2:** Substitute x = 2: - dy/dx = 2(2) + 3 = 4 + 3 = **7** That's your gradient at x = 2. **Why the wrong options tempt you** - **Option A (5):** You likely forgot to multiply the 2 in front of x, doing just 2 + 3 instead of 2(2) + 3. - **Option C (10):** You probably found y itself at x = 2 (which is 4 + 6 = 10) instead of finding dy/dx. Remember: gradient ≠ y-value! - **Option D (12):** Maybe you multiplied 2 × 2 × 3 incorrectly or confused the operations. **Quick takeaway** Gradient = differentiate first, then substitute the x-value — never substitute before differentiating!