Provide an appropriate response.Find all of the higher-order derivatives of x(t) = 
x3 - 
x2 - 4x. Use your graphing calculator to graph x(t) and x'(t) on the same axes. Verify that when x(t) is increasing (sloping upward), the value of x'(t) is positive. Repeat this for x'(t) and x''(t) and for x''(t) and x'''(t).
What will be an ideal response?
x'(t) = x2 - x - 4, x''(t) = 2x - 1, x'''(t) = 2, x(4)(t) = 0. All successive derivatives are also 0.
Mathematics
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