IB Maths.Second derivative. Gradient as rate of change

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Gradient as rate of change By the end of the lesson you will be able to: • Calculate the second derivative of a function. • Understand and use the derivative as rate of change.

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Transcript of IB Maths.Second derivative. Gradient as rate of change

  • 1. Gradient as rate of change Bytheendofthelessonyouwillbeableto: Calculatethesecondderivativeofafunction. Understandandusethederivativeasrateof change.

2. alsorepresentsthesecondderivativeofy withrespecttox. Thederivativeoff'(x)isdenotedf''(x)anditis calledthesecondderivativeoff(x)withrespecttox. 3. Giveny=3x4 5x,findthefirstandsecond derivativesofy. 4. Findf''(2)if 5. Aballisthrownfromthetopofabuilding.The distanceithasfallenaftertsecondsisrecordedand thefollowinggraphofdistanceagainsttimeis obtained. Calculatetheaveragespeedinthetime interval2 t4. distancetravelled timetaken averagespeed= 6. Calculatetheaveragespeedinthetimeinterval2 t4. 7. Calculatetheaveragespeedinthetimeinterval2 t3. Howcanwecalculatethespeedatt=2sec? 8. Thevelocityoftheballatanyinstantintimeisgivenby thegradientofthedisplacementtimegraph. 9. Thegradientrepresentstherateofchangeof displacementwithrespecttotime. rateofchange derivative rate:comparisonbetweentwoquantitieswithdifferentunits givestherateofchangeinywithrespecttox. 10. Ifdisplacementiss(t) instantaneousvelocity v(t)=s'(t)= instantaneousacceleration a(t)=v'(t)= Velocityistherateofchangeof displacementwithrespecttotime. Accelerationistherateofchangeof velocitywithrespecttotime. 11. Thedisplacementofabodyattimetsecondsis giveninmetresbys=2t3 t2 +2.Find: a)thevelocityofthebodyattimet. b)theinitialvelocityofthebody. c)theaccelerationafter1second. d)thetimeatwhichtheaccelerationiszero. 12. Thederivaterepresentstherateofchangeofa variablewithrespecttoanothervariable. Rateofchangeareacircle.ggb 13. Thederivaterepresentstherateofchangeofa variablewithrespecttoanothervariable. 14. Thenumberofdeer,N,inareserveismodelledby thefunction wheretisthenumber ofyearsafterthereservestarted.Findtherateof changeatwhichthepopulationisincreasing2years aftertheprogramstarted. 15. Bookpage366:Ex12D Ex.1to9 16. Attachments Rateofchangeareacircle.ggb


± Study Area - Nova Scotia · 2009. 7. 9. · King (2004). M. S. King Vertical Gradient (nT/m) Recommended Citation King, M.S. 2005: Airborne magnetic calculated first vertical derivative

± Study Area - Nova Scotia · 2009. 7. 9. · King (2004). M. S. King Vertical Gradient (nT/m) Recommended Citation King, M.S. 2005: Airborne magnetic calculated first vertical derivative

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Policy Gradient Methods: Pathwise Derivative Methods and ...rll.berkeley.edu/deeprlcourse/docs/lec7.pdfPolicy Gradient Methods vs Q-Function Regression Methods I Q-function regression

Tensor Analysis (H.1) Identities - Wikimedia Commons · Gradient of a vector [edit] See also: covariant derivative Since the total derivative of a vector field is a linear mapping

Tensor Analysis (H.1) Identities - Wikimedia Commons · Gradient of a vector [edit] See also: covariant derivative Since the total derivative of a vector field is a linear mapping

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gradient 1 gradient 2 gradient 3 gradient 4 ECDIS buyers · PDF file11 Type-specific ECDIS training 11 Technical training 11 Where should training take place? ... gradient 1 gradient

gradient 1 gradient 2 gradient 3 gradient 4 ECDIS buyers · PDF fileECDIS buyers guide gradient 1 gradient 2 gradient 3 gradient 4 gradient 1 gradient 2 gradient 3 gradient 4 10436

gradient 1 gradient 2 gradient 3 gradient 4 ECDIS buyers · PDF fileECDIS buyers guide gradient 1 gradient 2 gradient 3 gradient 4 gradient 1 gradient 2 gradient 3 gradient 4 10436

2. Gradient of a Chord & First Derivative

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Asynchronous Stochastic Gradient Descent with …Asynchronous Stochastic Gradient Descent with Delay Compensation will require the computation of the second-order derivative of the

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IB Maths.Turning points. Second derivative test

IB Maths.Turning points. Second derivative test

ECS171: Machine Learningchohsieh/teaching/ECS171_Winter...XGboost shows computing second order derivative yields better performance Algorithm: Computing the current gradient for each

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Steepest Gradient Method Conjugate Gradient Method

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1 Derivative Securities- Learning Objectives zWhat is a derivative security? zImportant characteristics of a derivative security; zMarkets for derivative.

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Structural optimization using sensitivity analysis and a ...allaire/levelset/report.pdf · 2.2 The shape derivative We apply a gradient method in order to calculate (7) by using the

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Partial Derivatives, Gradient, Divergence, and Curl Partial ......Partial Derivatives Recall that the derivative of a function of one variable provides information about how the function

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CHAPTER 9 Derivative Securities and Derivative …wps.aw.com/wps/media/objects/1232/1261732/protected/ch09/...186 Derivative Securities and Derivative Markets CHAPTER9 Many commentators

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Gradient-based Adversarial Attacks to Deep Neural Networks ...gradient generalizes the notion of the derivative to the case where the derivative is with respect to a vector: the gradient

Gradient-based Adversarial Attacks to Deep Neural Networks ...gradient generalizes the notion of the derivative to the case where the derivative is with respect to a vector: the gradient

A Derivative-Free Approximate Gradient Sampling Algorithm ...jnutini/documents/msc_talk.pdf · A Derivative-Free Approximate Gradient Sampling Algorithm for ... 2 jdkj!0, k #0 and

A Derivative-Free Approximate Gradient Sampling Algorithm ...jnutini/documents/msc_talk.pdf · A Derivative-Free Approximate Gradient Sampling Algorithm for ... 2 jdkj!0, k #0 and

A note about gradient descent: Consider the function f(x)=(x-x 0 ) 2 Its derivative is:

A note about gradient descent: Consider the function f(x)=(x-x 0 ) 2 Its derivative is:

cgu-odisha.ac.in · partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities,

cgu-odisha.ac.in · partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities,

S.NO CONTENTS PAGE NO UNIT-1 VECTOR …...MA6251 MATHEMATICS-II S.NO CONTENTS PAGE NO UNIT-1 VECTOR CALCULUS 1.1 Gradient-Directional Derivative 1 Problems 1.2. Divergence And …

S.NO CONTENTS PAGE NO UNIT-1 VECTOR …...MA6251 MATHEMATICS-II S.NO CONTENTS PAGE NO UNIT-1 VECTOR CALCULUS 1.1 Gradient-Directional Derivative 1 Problems 1.2. Divergence And …