Optimisation problems type 1: Finding absolute maximum and minimum of y = f(x) in a given closed interval [a, b]: To solve this problem, (a) Find critical points of f(x), and evaluate f at these points. (b) Find f(a) and f(b). The maximum value of items in (a) and (b) is the absolute maximum of f(x) in [a, b], and the minimum value of items in (a) and (b) is the absolute minimum of f(x) in [a, b].Please help solve this. follow up question would be the followingOptimisation problems type 2(First derivative test): Find local maximum and minimum of y = f(x) using first derivative: SIG787 Mathematics for AI Assignment 12025 Tri 1 Page 7 of 9 Find all critical points of f(x). If for a critical point x = c, f changes from positive to negative (f changes from increasing to decreasing), x = c is a local maximum point. If for a critical point x = c, f changes from negative to positive (f changes from decreasing to increasing), x = c is a local minimum point. Optimisation problems type 2(Second derivative test): Find local maximum and minimum of y = f(x) using second derivative: Find all critical points of f(x). For a critical point x = c, if f (c)=0 and f (c)>0, x = c is a local minimum. For a critical point x = c, if f (c)=0 and f (c)<0, x = c is a local maximum. if f (c)=0, the test is inconclusive. It does not give any useful information, and we need to use other techniques to decide the type of stationary point.