(Solved):   a) Consider the function \( \mathbf{f}(\mathbf{x})=3 \mathrm{x}^{2}-6 \mathrm{x}+5 \). Det ...

 

a) Consider the function \( \mathbf{f}(\mathbf{x})=3 \mathrm{x}^{2}-6 \mathrm{x}+5 \). Determine the lowest and highest values of this function in the interval \( [0,3] \) (refer to lecture 9 for details about how to find the maximum and minimum value of a function). Write down the steps of the solution. [8 marks] b) Explain the concept of the gradient descent method with a help of a suitable example. [9 marks] c) Explain the main advantage of the gradient descent method as compared to the first derivative test for finding the maximum and minimum of a function. [8 marks] \( d \) T Consider the function \( \mathbf{f}=3 \mathrm{x}^{2} \). Assume that the learning rate \( \alpha=0.1 \) and the initial value is \( \mathbf{x}=2 \). Using this information, show the first 3 iterations