To be answered perfectly complete solution:

I. Find all critical points of the given function f. SHOW YOUR SOLUTION (a) f(x)=4x2 - 3x + 7 (b) f(x)=3x4 - 5x + 6 (c) f(x)=12x5 + 4x2+x + 10 II. Find the extrema of the given functions on the interval [1, 1]. SHOW YOUR SOLUTION (a) f(x)=5x2 + 2x + 5 (b) f(x)=2x2 - 2x + 8Topic: CRITICAL POINTS AND POINTS WHERE EXTREMA OCCUR Here, we define several concepts. We will see later that extreme points occur at critical points. ion Definition Let / be a function that is continuous on an open interval / containing 20. " We say that 20 is a critical point of f if /'(xo) == 0 or /'(xo) does not exist (that is, f has a corner or a cusp at (ro, f(ro))). . We say that the maximum occurs at ro if the value /(20) is the largest among all other functional values on /, that is, /(xo) 2 /(x) for all x e I. . We say that the minimum of / occurs at r; if the value /(ag) is the smallest among all the other functional values on /, that is, f(zo)