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I can assist with solving or explaining the mathematical problems shown in the image. Let me analyze the content and provide solutions to each question step by step.

### Problems on the Image:

1. **Question 7**: \( f(x) = x^2 \sqrt{16 - x^2} \)
   - The derivative of the function is being worked out.
   
2. **Question 8**: \( y = \sqrt{5x^2 + 3} \), and the task is to find \( \frac{d^2y}{dx^2} \).
   
3. **Question 9**: This asks to find the equation of the lines relative to the curve \( y = \sqrt{x^2 + x - 4} \) at \( x = 3 \):
   - Part (a): Find the tangent line.
   - Part (b): Find the perpendicular line.

4. **Question 10**: Find the point(s) of horizontal tangency for \( f(x) = \left( \frac{x - 3}{x + 5} \right)^2 \).

5. **Question 11**: Find the point(s) of horizontal tangency for \( f(x) = \frac{2}{\sqrt[3]{x^2 + 4x - 4}} \).

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Find the equation of the lines relative to the curve y = √(x² + x - 4) at x = 3. Show necessary work: a) tangent b) perpendicular.

Explore how to find the equations of the tangent and perpendicular lines to the curve y = √(x² + x - 4) at the point where x = 3. This problem involves calculating derivatives and applying key geometric principles, making it suitable for high school students in Grades 11-12.

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