Explanation Given: y = f ( x ) = 5 x 2 + 6 x − 4 We know that the critical points are the points at which the derivatives of the function become zero or undefined. Here, the given function is y = f ( x ) = 5 x 2 + 6 x − 4 Differentiating the above function with respect to x, we get f ' ( x ) = d d x ( 5 x 2 + 6 x − 4 ) = ( 10 x + 6 ) To find out the critical points, we equate the above equation to zero. i.e. f ' ( x ) = 0 10 x + 6 = 0 x = − 3 5<

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.3, Problem 28E

To determine

To find all the critical points of the function y=5x2+6x−4 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

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Chapter 4.3, Problem 27E

Chapter 4.3, Problem 29E

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Find any critical numbers for the function f(x) = (x+6)10 and then use the second-derivative test to decide whether the critical numbers lead to relative maxima or relative minima. If the second-derivative test gives no information, use the first-derivative test instead. Find any critical numbers for the function f(x) = (x+6)10. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical number(s) of f(x) is/are x =]. (Use a comma to separate answers as needed.) B. There are no critical numbers. Decide whether the critical numbers lead to relative maxima or relative minima. Select the correct choice below. A. There is a relative maximum at the critical number. B. There is a relative minimum at the critical number. C. There is neither a relative maximum nor a relative minimum at the critical number. D. It cannot be determined if the critical number leads to a relative maxima or minima.

Chapter 4 Solutions

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To find all the critical points of the function y = 5 x 2 + 6 x − 4 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

Solution Summary: The author explains that the critical points are the points at which the derivatives of the function become zero or undefined.

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To find all the critical points of the function y=5x2+6x−4 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

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Chapter 4 Solutions