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3.5_Higher_OrderDerivatives_summer

# 3.5_Higher_OrderDerivatives_summer - (14t 5 • Find the...

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3.5 Higher Order Derivatives The derivative of f(x) is denoted by f’(x) and will now be called the “first” derivative of f. The derivative of f’(x) is denoted by f”(x) and will now be called the “second” derivative of f. The derivative of f”(x) is denoted by f’’’(x) and will now be called the “third” derivative of f. For the function f(x) = x 5 –x 4 –x 3 + x 2 – x – 1, The first derivative of f at x is: The second derivative of f at x is: The third derivative of f(x) = 3x 4 –5 x 3 is If f(u) = (4 – 3u) (1/2 ), Then f’(u) = (-3/2) (4 – 3u) ( - ½). Find the second derivative of f(u). If f(s) = (s – 6)/(s+6), Find the first derivative of f(s). f’(s) = Find the second derivative of f(s). f”(s) =

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If f(t) = (7t 2 + 5t +2) (19/10 ), then f’(t) = (19/10) (7t 2 + 5t +2) (9/10
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Unformatted text preview: )(14t + 5), • Find the second derivative of f at t • f”(t) = The number of persons aged 18-64 receiving disability benefits • Through social Security , the Supplemental Security Income, or both, from 1990 through 2000 is approximated by the function: • N(t) = 0.00034t 3 + 0.768t 2 + 0.70t + 5.7, where N(t) is in millions and t is in years with t=0 corresponding to the beginning of 1990. Find: N(8); N’(8); N”(8) {Round to nearest thousandth} 60.626; 13.053; 1.552 • During the construction of an office building, a hammer is accidentally Dropped from a height of 576 ft. The distance the hammer falls in t seconds is given by s = 16 t 2 . • What is the hammer’s velocity when it strikes the ground? (32)(6)= 192 • What is its acceleration? 32...
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3.5_Higher_OrderDerivatives_summer - (14t 5 • Find the...

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