Find the relative extreme points of the function, if they exist. Then sketch a g

Question

Find the relative extreme points of the function, if they exist. Then sketch a graph of the function. f(x) = x^2 + 2x + 3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The relative minimum point(s) is/are and the relative maximum points(s) is/are. B. The relative maximum point(s) is/are and there are no relative minimum points. C. The relative minimum point(s) is/are and there are no relative maximum points. D. There are no relative minimum points and there are no relative maximum points. Choose the correct graph below. A. B. C. D.

Explanation / Answer

given f(x) = x2+2x+3 : f ' ( x) = 2x+3 =0 for extreme values

2x = -3 and x = - 3/2 find f ''(x) = 2 >0 for allx hence for x= -3/2

hence x = - 3/2 is the pont of minimum ANS : C

correct graph is A the function has minimum value at x= -3/2

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