Question

(1 point) Consider the function f(x) = -22% + 36x? - 162x + 10. This function has two critical numbers A <B: А 3 and B 9 f"(A) 36 f"(B) = -36 Thus f(x) has a local -206 and a local 10 at A (type in MAX or MIN) at B (type in MAX or MIN).

Answer 1

selt f(x)-- - 21² + 36*_1622 +10 we first need the derivative of the function freie ting- 720 て9) our derivative is a polynomial and so will exist everywhere critical flal=0 point -cart 720-162 = tzt url -k O= X-9x - 32 +27 - 0 > (X-9) - 3 (x-9) = 0 (2-7) (x-3) n = 3,9 A = 3; B=9 (ACB) Il f (x) Now finding کہ وہ f(x)= -120 +72 36 (8) -367 72 & (9) -108 + 72 = -36

local maximum and minimum value finding at a=3 -263)*+ 3613) – 16213) 710 F03) -54 + 324 486 + 10 - -540 + 334 206 206 local minimum value Il at a-9 f(9) at 11 - 2 (9)3 + 36 (99_162 (9) +10 -1/458 14/58 t 2/1916 +10 10 local mani mum valina