Explanation Given: The function is f ( x ) = − 3 x 2 − 3 x + 11 . Formula used: According to the first derivative test, if c is the only critical number of the given function for an interval [ a , b ] such that a < c < b . Consider, f is differential for every value of x in the interval except at x = c . 1. For f ′ ( a ) > 0 and f ′ ( b ) < 0 , there will be a local maxima at c . 2. For f ′ ( a ) < 0 and f ′ ( b ) > 0 , there will be a local minima at c . 3. There will be no local extrema when f ′ ( a ) and f ′ ( b ) are either both positive or both negative. Calculation: Solve the given function: f ( x ) = − 3 x 2 − 3 x + 11 Differentiate the above function: f ′ ( x ) = − 6 x − 3 Substitute 0 for f ′ ( x ) . − 6 x − 3 = 0 6 x = − 3 x = − 3 6 = − 1 2 Use first derivative test on − 1 2 to determine the local extrema of the given function

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ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 12, Problem 6RE

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To calculate: The largest open integral for which the function f(x)=−3x2−3x+11 is increasing or decreasing.

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Chapter 12, Problem 5RE

Chapter 12, Problem 7RE

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Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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The largest open integral for which the function f ( x ) = − 3 x 2 − 3 x + 11 is increasing or decreasing.

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To calculate: The largest open integral for which the function f(x)=−3x2−3x+11 is increasing or decreasing.

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Chapter 12 Solutions