Let f(x) = 2x³ – 1822 – 240x. Complete this problem without a graphing calculator. (a) The derivative of f(x) is f'(x) = (b) As a comma-separated list, the critical points of ƒ are x = Since f is continuous on the closed interval [-5, 18], f has both an absolute maximum and an absolute minimum on the interval [-5, 18] according to the Extreme Value Theorem. To find the extreme values, we evaluate f at the endpoints and at the critical points. (c) As a comma-separated list, the y-values corresponding to the critical points and endpoints are y =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.