Consider the following function. f(x) = 2x^3 - 21x^2 + 60x - 9 Find the derivative. f'(x) = Find any critical numbers of the function. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE) x = Find the interval(s) on which f is increasing. (Enter your answer using interval notation.) Find the Interval(s) on which f is decreasing. (Enter your answer using interval notation.) Find the local minimum and maximum value of f. local minimum value local maximum value
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Given function f(x) = 2x^3 - 21x^2 + 60x Now, let's find the first derivative, f'(x): f'(x) = d/dx(2x^3 - 21x^2 + 60x) = 6x^2 - 42x + 60 Now, let's find the second derivative, f''(x): f''(x) = d/dx(6x^2 - 42x + 60) = 12x - 42 Now, let's find the critical Show more…
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