1 long question with 2 parts

Part A

Let f(x) = 6 . We will use the definition of derivative to find the deivative of f () (i) What is the definition of derivative of f (z) ? Of (2) = f(ath)-f(z) h Of' (z) = lim f(@th)-f(x-h) h-+0 h Of'(x) = lim f(ath)-f(z) h-+0 h Of'(x) = lim f(2+2 h)-f(eth) h-+0 2 h (ii) Which one is the correct statement (the next step to find f (x) by definition)? 6 Of ( z ) = (th)2 h 6 Off(x) = lim (eth)2-22 h-0 h 6 O f'(z) = lim (ath)2 h-+0 h 6 Off(z) = lim (2+2h)2 h-+0 h (ili) Which one is the correct statement (the next step to find f)(x) by definition)? Of'(z) = lim 6((* + h)2 - 22) h 0 hx2(x+h)2 Of'(x) = lim 6 h Oh((ath)2 - 22) Of'(x) = lim 6(12 - (x + h)2) h 0 hx2(x+h)2 of (z) = lim 6 h-Oh(rth-z)2 (iv) Which one is the correct statement (the next step to find f (x) by definition)? -6h(2x + h) Of (z) = lim h-0 x2(x+h)2 of'(z) = lim -6(2x + h) h +0 hx2(x+h)2 of(z) = lim -6(2x + h) h-0 x2(x+h)2 Of'(z) = lim - 6(2x + h) h-0x2(x+h)2Let f(z) = vr + 29 . We will use the definition of derivative to find the derivative of f (). (i) What is the definition of derivative of f (x) ? Of' (x) = lim f(ath) - f(x -h) h-+0 h Of'(x) = lim f(ath)- f(z) h-+0 h Of'(2) = f(ath)-f(2) h Of'(x) = lim /(2+2 h)-f(xth) h-+0 2 h (ii) Which one is the correct statement (the next step to find f/() by definition)? Of'(z) - Vath+ 29 - vx + 29 h Of'(z) = lim vath+ 29- va+ 29 h-0 h Of (x) = lim vrth+29- vx - h+ 29 h-+0 h of'(z) = lim vr + 29 +h - vx+ 29 h-0 h (ii) Which one is the correct statement (the next step to find f/(x) by definition)? of(x) = lim - rth h-Oh(vx +h + 29 + vx +29) of'(x) = lim h h Oh(vx +h + 29 - vx + 29) of'(x) = lim 2h h-Oh(vr +h + 29 + vx +29) of'(z) = lim h h-Oh(vr + h + 29 + vx+ 29) (iv) Which one is the correct statement (the next step to find f (a) by definition)? 29 of (x) = 2vi + 29 of (x) = - 2 Vi + 29 of(x) =. 1 2vrth of (z) = 1 2vx + 29