Solve using Python, please.

Section B- Minimize the following function instead: f(x, y) = 3x2 + 5y2 +5x3 1) Define the function and its analytical gradient in Jupyter notebook. ( 2 marks) 2) Implement a steepest gradient algorithm. Use Xo = 2, yo = 20 as starting points. You can consider that the algorithm has converged to a solution if f(x,y) is within 0.0001 of its optimal value. (4 marks). 3) BONUS (2 marks): Plot the value of f(x,y), x, and y. For example: MECH203 - Mathematical and Computational Tools for Mechanical Engineers II Second landscape V 12 -0.2 0.0 0.2 0.4 0.6 0.8 10 (you should insert better labels and legends.) 4) Use the CG and BFGS algorithms available in the SciPy.optimize.minimize module. Use Xo = 2, yo = 20 as starting points. (4 marks). 5) How many minima does this function have? (2 marks) 6) Can the computer find them all? (2 marks) 7) Are they local or global? (2 marks) Section B- Minimize the following function instead: f(x, y) = 3x2 + 5y2 +5x3 1) Define the function and its analytical gradient in Jupyter notebook. ( 2 marks) 2) Implement a steepest gradient algorithm. Use Xo = 2, yo = 20 as starting points. You can consider that the algorithm has converged to a solution if f(x,y) is within 0.0001 of its optimal value. (4 marks). 3) BONUS (2 marks): Plot the value of f(x,y), x, and y. For example: MECH203 - Mathematical and Computational Tools for Mechanical Engineers II Second landscape V 12 -0.2 0.0 0.2 0.4 0.6 0.8 10 (you should insert better labels and legends.) 4) Use the CG and BFGS algorithms available in the SciPy.optimize.minimize module. Use Xo = 2, yo = 20 as starting points. (4 marks). 5) How many minima does this function have? (2 marks) 6) Can the computer find them all? (2 marks) 7) Are they local or global? (2 marks)