MAT135H1 Lecture 7: 3.1 Higher Order Derivatives (3)
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MAT135H1 Full Course Notes
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3. 1 higher order derivatives, velocity, and acceleration: the derivative of the derivative function is called the ________________________________________ secondderivative, notation: f cx y. Example 1: determine the second derivative of f x x. 2 ttx 3 i c q: one application of derivatives is with regards to the motion of objects (physics application) s t. If if v 41 0 if vct object netmoving at rest moving in positive directroir. 0 if vce lo moving in negative direction. If if act o constantvelocity if act o velocity is increasing if act lo velocity is decreasing. Example 2: the position of an object is given by s t t ( ) 6. 0: determine the object"s velocity and acceleration at any time, t, in seconds t. 12671ah t s 4: at what time is the object at rest? v t o. 6 o 2 t o initial time: 3 the intral position is 0.
