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Calculus Section 3.7 Find higher ordered derivatives.

Calculus Section 3.7 Find higher ordered derivatives. Higher order derivative notation 1 st derivative: y’ f’(x) dy / dx D x y 2 nd derivative: y’’ f’’(x) d 2 y/dx 2 D x 2 y

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Calculus Section 3.7 Find higher ordered derivatives.

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  1. Calculus Section 3.7Find higher ordered derivatives. Higher order derivative notation 1st derivative: y’ f’(x) dy/dxDxy 2nd derivative: y’’ f’’(x) d2y/dx2Dx2y 3rd derivative: y’’’ f’’’(x) d3y/dx3Dx3y 4th derivative: y(4)f(4)(x) d4y/dx4Dx4y Find d4y/dx4 y = 2x6 + 3x5 – 7x4 + x3 – 5x2 + 7x - 9 Find y’’ if y = 10x5/2

  2. Find the indicated derivative. Find f’’ if f(x) = x+4 x-3 Find f’’(x) if f(x) = (3x+7)4

  3. Instantaneous acceleration is the rate of change of velocity. If s(t) is the distance function, then s’’(t) is the acceleration function. The height of a ball is given by 400 – 16t2. Find the acceleration after 2 seconds.

  4. example The distance a mouse is from its starting point is given by the function s(t) = t3 – 2t2 + 6t where s is the distance in feet and t is the time in seconds. a. Find the distance at 3 seconds. b. Find the velocity at 3 seconds. c. Find the acceleration at 3 seconds.

  5. assignment Page 157 Problems 2 – 40 even

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