Which statement is true? of(x) = x + 3x + 6 is differentiable everywhere. of (x) = + is differentiable at x = 0. o Iff (x) is differentiable at x = c, the lim f ( xth ) -f(x ) can not be 0. h-c h o f(x) = tan(x) is differentiable everywhere. 2 3 4 5 MacBook Air 44 F8 20 F5 F6 F7 F2 F3 F4 F1 % A & @ # 6 8 2 3 4 5 7 Y U Q W E RMany diabetics need to control their blood sugar levels with insulin. A graph is given that shows blood sugar levels over time after insulin is given to a non-diabetic person at time, t = 15 minutes. As you can see insulin causes blood sugar levels to drop. Where is the function not differentiable and why? Blood Sugar Levels 15 30 45 60 75 90 105 120 Time O The function is differentiable everywhere except t = 15, t = 30, and t = 40 where there are corners. The function is differentiable everywhere. O The function is differentiable everywhere except at t - 15 where there is a discontinuity. The function is differentiable everywhere except t - 30 2 3 4 5 6 7 8 9 10 Next MacBook Air 44 DII F5 F7 F8 F9 F10 880 F4 F2 a # $ 8 9 O 5 O 2 3 4 P W E T Y U O R L K S D F G H B Z X C V N Mfferentiability Which statement below is true? O If a graph is continuous then it must be differentiable. O A cusp is a point where the graph is not continuous. O If a function is differentiable everywhere then it must be continuous. O It is possible for a function to be differentiable but not continuous. 1 MacBook Airrentiability f(x) = lim/(xth) -f(x) h-0 h 14Diff (x) = |x|. Use the definition of the derivative to determine if the function is differentiable at x o f (x) is not differentiable at x = 0 because the lim = 00 at x = 0. h-0 h of (x) is differentiable at x = 0. o f(x) is not differentiable at x = 0 because the lim (xth)-f(x) h - is not the same from the right and left. h-c o f(x) is not differentiable at x = 0 because the lim (xth)-f(x) h increases without bound at x = 0. h-c 1 2 3 4 5 6 9 10 Next > MacBook Air 44 DIL FB F9 F10 20 F6 F7 F2 F3 F4 F5 F1 & @ # O 5 6 N 4 R T Y U O P W E K F H J S D F G