19 *Continuity / Differentiability ProblemEX#1 :fx x2,x36x9,x3 At 3 fx 3 296 3 99At 3 limx3fx limx3fx f3 9. Therefore f (x) is continuous. f (x) is continuous iff both halves of the function have the same answer at the breaking point.fx 2x,x36,x3 At 3 f(x)2 3 666At 3 both halves of the derivative = 6. f (x) is differentiable if and only if the derivative Therefore the function is differentiable. of both halves of the function have the same answer at the breaking point.Since both sides of f x and fx agree at 3, then f x is continuous and differentiable at x3.*Rectilinear Motion (Position, Velocity, Acceleration Problems) -We designate position as x t, y t, or s t.-The derivative of position, xtv tvelocity.-The derivative of velocity, vta tacceleration.-We often talk about position, velocity, and acceleration when we’re discussing particles moving along the x-axis or y-axis.-A particle is at rest or is changing direction when v t0.-A particle is moving to the right or up when v t0 and to the left or down when v t0.-To find the average velocity of a particle 1bav(t ) dtab-To find the maximum or minimum acceleration of a particle set at 0, then check the values on a number line to see if and how they switch signs.-Speed is the absolute value of velocity, v t.If v t and a t agree v ta t speed is increasing. If v t and a t disagreev ta t speed is decreasing.