Explanation Given information: The function is as expressed as follows: f ( x ) = 1 3 x 3 + 1 2 a x 2 + b x + c ...... (1) Calculation: The given function f ( x ) is the cubic polynomial. The domain of the function is ( − ∞ , ∞ ) because the function is defined for all real values of x . Differentiate the equation (1) as shown below. d d x f ( x ) = d d x ( 1 3 x 3 + 1 2 a x 2 + b x + c ) f ′ ( x ) = 3 x 2 3 + 2 a x 2 + b f ′ ( x ) = x 2 + a x + b To obtain the critical point, equate the derivative of function f ( x ) to 0. f ′ ( x ) = 0 x 2 + a x + b = 0 By completing the square, simplify the above equation. x 2 + a x + b + ( a 2 ) 2 − ( a 2 ) 2 = 0 x 2 + a x + ( a 2 ) 2 = ( a 2 ) 2 − b ( x + a 2

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

21st Edition

ISBN: 9781319438333

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.2, Problem 99E

To determine

To find:

The condition on coefficients a and b of the cubic polynomial f(x)=13x3+12ax2+bx+c such that the function f(x) has neither a local minima nor maxima.

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Chapter 4.2, Problem 98E

Chapter 4.2, Problem 100E

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Chapter 4 Solutions

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

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The condition on coefficients a and b of the cubic polynomial f ( x ) = 1 3 x 3 + 1 2 a x 2 + b x + c such that the function f ( x ) has neither a local minima nor maxima .

Solution Summary: The author explains the condition on coefficients of the cubic polynomial f(x) such that the function has neither a local minima nor maxima.

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The condition on coefficients a and b of the cubic polynomial f(x)=13x3+12ax2+bx+c such that the function f(x) has neither a local minima nor maxima.

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Chapter 4 Solutions

The condition on coefficients a and b of the cubic polynomial f ( x ) = 1 3 x 3 + 1 2 a x 2 + b x + c such that the function f ( x ) has neither a local minima nor maxima .

Solution Summary: The author explains the condition on coefficients of the cubic polynomial f(x) such that the function has neither a local minima nor maxima.

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To find: The condition on coefficients a and b of the cubic polynomial f(x)=13x3+12ax2+bx+c such that the function f(x) has neither a local minima nor maxima.

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Chapter 4 Solutions

To find:

The condition on coefficients a and b of the cubic polynomial f(x)=13x3+12ax2+bx+c such that the function f(x) has neither a local minima nor maxima.