Explanation Given: The function is f ( x ) = x − 1 2 x + x + 4 . The value of x is 2.3 . Definition used: 1. The first derivative of the function is the differentiation of the function f ′ ( x ) = d d x f ( x ) . 2. The second derivative of the function is the differentiation of the first derivative of the function f ″ ( x ) = d d x f ′ ( x ) . The chain rule stated that the derivation of the function, f ( g ( x ) ) is f ′ ( g ( x ) ) ⋅ g ′ ( x ) . Formula used: Derivative of power rule: d d x a x n = a ⋅ n ⋅ x n − 1 The quotient rule of the derivative d d x ( u v ) = v d u d x − u d v d x v 2 . Calculation: The given function is f ( x ) = x − 1 2 x + x + 4 . Differentiate f ( x ) = x − 1 2 x + x + 4 with respect to x on both sides, f ′ ( x ) = d d x [ x − 1 2 x + x + 4 ] = ( 2 x + x + 4 ) d d x ( x − 1 ) − ( x − 1 ) d d x ( 2 x + x + 4 ) ( 2 x + x + 4 ) 2 ( Use qoutient rule ) = ( 2 x + x + 4 ) ( 1 2 x ) − ( x − 1 ) ( 2 + 1 2 x ) ( 2 x + x + 4 ) 2 ( Use power rule ) = ( x + 1 2 + 2 x ) − ( 2 x + 1 2 − 2 − 1 2 x ) ( 2 x + x + 4 ) 2 Further the simplification of the above equation is, f ′ ( x ) = x + 1 2 + 2 x − 2 x − 1 2 + 2 + 1 2 x ( 2 x + x + 4 ) 2 = − x + 2 + 5 2 x ( 2 x + x + 4 ) 2 Differentiate f ′ ( x ) = − x + 2 + 5 2 x ( 2

Applied Calculus for the Managerial, Life, and Social Sciences

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ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Applied Calculus for the Managerial, Life, and Social Sciences

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The value of second derivative of the function at given value of x .

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