Question

Please explain step by step in a dumbed down version -- if you can

Based on the graph f(t) sketched to the left, (a) fill out approximate values in the table of A(x) = $* f(t)dt. (b) For what value of x in the interval (0,4] does A(x) reach a minimum? (Hint 1. you see the graph of f(t) not A(x). Hint 2. A(2) is not the minimum. ) y = f(t) 1 (c) Sketch an approximate graph of the area function A(x) restricted to the interval (0,4). A(0) A(1) A(2) A(2.75) | A(3) A(4)

Answer 1

2 A 12) = fit) shoot Alor- 1 flak Alo) = 0 2.15 2 + + + 3 4 1 All) = s tiedt A 0 we can Area of between o to 1, a triangle shown in it by fla) approximate figure (Area of a triangle) 1 0 Ali) 2 / 3 x 1 x 1 - [by graph 0.5 A(1) + -- 2 AL2) me have of fladt. A12) (fies de 0.5t se fledt to calculate & the Approximation & flt) dd clearly again con appennoximate ky the (Area of triangle) - (Area AJ ue and it 1 2 (by as graph -17

$1*3** - 1 ***:) -0.5. Sa A 12) 0.5+ (-0.5) A(2) NALD for A(2.75) 2-75 A (2.75= fltati 2.75 fltdt. flt dto + fltd 2 275 A12-75) 0.5 -0.5 + fitlat 2 2.75 A(275) s, f14)* 2 2.75 can Again is Approximate 5. For to Area of the triangle) 2 2.75 12.75 S] 1/2 x 12.75-2) x 1 fladt -1 - 0.540-75 -0.375 (by graph ) 11

By ③ A12.75) -0.375 Now for A13) A13) - A 12.75) + f(t) dt. 언 2.75 ie A13) - flest su 2 fluidt t s 2.75 fissat fltidt. + 2.75 3 A13) ~ AL2.75) fledt 2.75 A 13) - - 0.375 + 1 x (3-2.75) *0.5 2 AB Approximate by the Area of ie 2.75 3 A13) ~ -0.373 + 12 / 2 x 0.25% 0.9 0.11 25 A13) -0.375+ A 13) -0.2625

Alu) 275 fit) at + s f1t)dt. 2.75 4 Alug w A 12.75) fit) dt. + so 2.75 Alu) -0.375 t fladt. Les fueron 2.75 Alu) ~ - 0.375 + 1 / 2 (4-2-75) 45 Area triangle of 4 2.75 Alu - - 0.375 +0.5x 1.2585 Alu) -0.375+ 3.125 A14) 2-75 Mence ALL) A 12:75) A13) AG) ALI) Alo) - 0.375 -0.26 2.75 0 0.5 is minimum Area the clearly to 2.75 ( By graph and By calculations 0 from of part (as) ber x = 2.75 A(2) is minimum.

A12) the For for a trou] graph of and A(2) 20 Aco) clearly A(1) = 0.5 A (3) = – 0.26 ) A (2.75) = – 0.375 Alu)= 2.75 graph is increasing blw oto 1 th increasing ). IAS 1 to = 2.75 blw 4 decreasing increasing blw 2.750 to then A(2) 2.75 0 -315