Determine the location of each local extremum of the function. [ f(x)=frac{2}{3} x^{3}-frac{9}{2} x^{2}+4 x+3 ] What is/are the local minimum/minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The local minimum/minima is/are ( square ) at ( mathrm{x}= ) ( square ) . (Use a comma to separate answers as needed. Type integers or simplified fractions.) B. The function has no local minimum.
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Given the function \[ f(x)=\frac{2}{3} x^{3}-\frac{9}{2} x^{2}+4 x+3, \] its first derivative \( f'(x) \) can be found using the power rule. The derivative of \( x^n \) is \( nx^{n-1} \), so applying this rule to each term gives: \[ f'(x) = \frac{2}{3} \cdot Show moreā¦
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