Calculus Section 3.7 Find higher ordered derivatives.

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Presentation transcript:

Calculus Section 3.7 Find higher ordered derivatives. Higher order derivative notation 1st derivative: y’ f’(x) dy/dx Dxy 2nd derivative: y’’ f’’(x) d2y/dx2 Dx2y 3rd derivative: y’’’ f’’’(x) d3y/dx3 Dx3y 4th derivative: y(4) f(4)(x) d4y/dx4 Dx4y Find d4y/dx4 y = 2x6 + 3x5 – 7x4 + x3 – 5x2 + 7x - 9 Find y’’ if y = 10x5/2

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

Instantaneous acceleration is the rate of change of velocity 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.

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.

assignment Page 157 Problems 2 – 40 even