Question

6. (10 pts) Use calculus to sketch the graph of f(x) = 6.5-3x Show clearly the (x, y) coordinates of all (-) and x +0. You must show local max, local min, and inflection points. Show clearly the behavior as x ALL work that justifies the shape of your graph.

Answer 1

a. use calcular to sketch the hraph of f(n) = x² – 3x16.5. Show clearly the (x, y) coordinate of all local max, local min, and inflection pointy. show cleany the behaviour as n (hool and a lto You noot show All work that Justifies the shape of your work. soni- briven, Alw=2-3* +6,5 since, we have to draw the braph so, we will first tind critical points ie where graph derivative ip equal. to yetu. FIN) = 2-3x+605. f(n) = 2 -3 70 F'in) = x-3 - 0 Ia=37 Hence, n=3 it the point where derivative is to. since, It is quadratic equation, whose coefficient of x² is ļ, and it is positive, so the braph of quadratic equation ip Concave upward .

- Stepp af hraph Fliml=0 n-3 -6 [n=3) derivative is reno and to find the point of gollection fle(n)=0 : : f(n)= x² – 3x+6.5 t'lu) = 27-3 = x-3. flim = 1 2 no such gt shows that there in pointy of infection.

4 2.5 2 2.5 flm)= x2 - 3x165. 11,4) 13,2) since, hraph is cuncare upward , and darivative ip ren at only & pt: so, the this Graph hop only Local minina, at n=3 f(n) = -31 tbs. - F13) - 9 - 9t6.5 = 2

Hence, Local minima is 2 . so required coordinate it 1 (32) Since, domain in nt (-0,ool. Ranges at f(3) = 2 Fla) = a in domain of (roo, oof graph pun, [2,007, 24/9722