Question

Mailings AR Assignment Compatibility Mode Microsoft Word non-commercial use Review View E 21 Aabbcc AaBbc Emphasis Heading 1 Normal Paragraph (10 marks) Subtitle Title Strong Styles ant: Late submission will NOT to be entertained. f(x) = x - 3x² + 1. (1) Find the first and second derivatives. (2 marks) (ii) Find all interval(s) on which f(x) is increasing or decreasing and minimum and maximum points. (5 marks) (iii) Find all interval(s) on which the graph of f(x) is concave up and concave down and also the inflection point. (4 marks) (iv) Sketch the graph for f(x), labeling the critical and inflection points. (4 marks)

Answer 1

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-)f(x) = x² 3x²+1 f'(x): 3*?- 6x f"(x)= 62-6 1) f'(X= 0 => 326* =O 3x(x-2)=0 > X:0,2 Interval (-oo_o) I (0, 2) I (200) sign off + I- Therapeuting Incre. Decreased Incora f(0): 0-0+1=1 f(2)= 2% 3x4 +1: 8-12+13 -3 n f'(x)= 0 =) 6X-6 -6 x=1.. Interval I (-es, 1) I (1 ). Sianoff" - + up/ down Down I up

I combining above Intervals I (-0,0) Inc./Dec. | In. Up/Down I Doan 20) = 1, f(2)=-3 tables (0, 1) (1, 2) De. De. Doan up fl)= -1. In. up ya local maximum Inflection poiar (1,-1) (2-3) local minimum