Question

Find the value of the derivative (if it exists) at the indicated extremum. (-3,-6) so Sodo -6 The derivative does not exist None of these None of un- - -- - - from the graph whe - Determine from the graph whether f possesses extrema on the interval (a, b). I b ; ܦ݁ ; ܦܶ ܒ݁ܶܗ ܘ Maximum at x-c; minimum at x=b Maximum at x=c; no minimum No maximum; minimum at x=b No extrema None of these

Answer 1

I we have to kind derivative of this graph att 12 -8 -4 (x, y) = (-3,-6) (3,6) 5+ since; it is the extremum point on the given graph so f'(x) at x =-3, y=-6 soj dy o so; correct option is is parallel to x-axis dx - 6.0 ous. a cb have to find auore we few possess extrema on the interval (a, b).

since . - • shows shows included excluded so from we and the ginen see that there is graph of maximum aut no minima fou) a=6 - so; Cossect option is (6.) (maximum at X=6; no minimum minimam Point we the have given to graph defere mine whether possess extrema on (a, b) - - soj from Minimum So Cosrect the graph at sea option is we see that . and no maxima. (c) No maxm, minimum atua 3 we the have to Zme tim To get find all feu) = critical critical numbers for (atz" (4-1) 4 number's we differantiale - to n then 00 heake bro 1.1. f'(n) = 0 au 1/(442) ?(x43) Cat B 117)++3=D (x+25² (x-1)3 [4 Cutz) + 304-1)]=0

(x+232 (x-1)} (ants=0 So, x=-2 , n=1, n =- is (d.) (-2, 1,-1/2 Soi esiven, correct option fin) = 9-14 (6) we Then have to that find t'(c) c = interval (217) in the f(7) a f(2) f(7) = 9-14 = 7 f (2) = 9-14 = 2 So; f'll) = 7-2 - 7-2 iz c +514 $o, correct option