Answer Happy

41. [2/11 Points] DETAILS EXAMPLE 4 Video Example Find the derivative of the function f(x) = x2 - 9x + 2 at the numbers (a) 3 and (b) a. SOLUTION (a) From this definition we have the following. f(3 + h) - f(3) f(3) = lim h0 h - 1) - 3603 + n) + 2] - [(3)2 – 943) + 2] - 9(3 + h) ()) ] = lim h-0 h 9 + h² +6h 27 - 9h + 2 + 16 lim h→0 In²th = lim h0 h II lim h0 (h+1 = 4 1

(b) fa) lim f(a+h)-f(a) h0 h ICE (a ) 1 -96 + n) +2] -102 - 98 + 2) a +h2 (a + h) + lim -0 n a2 + h2 - 9a - 9h + 2 - a2 + 9a - 2 - + 2ah = lim - 0 h h2 + 2ah-5h = lim h0 h = lim h 0 - ... ) h + 2a – 5 ) h - 5 29-5 As a check on our work in part (a), notice that if we let a = 3, then f'(a) = f'(3) = 1

26. [1/2 Points] DETAILS PREVIOUS ANSWERS SCALCET9 2.5.019. Explain why the function is discontinuous at the given number a. (Select all that apply.) 1 f(x) a = -4 x + 4 lim f(-4) and lim f(x) are finite, but are not equal. X-4 f(x) and lim f(x) are not finite, and are not equal. X-4 f-4) is undefined. lim f(x) does not exist. x---4+ none of the above X