Explanation Proof: Given information: The equation that relates the thickness of cortex of children with their ages (in year) is given by, S ( t ) = 0.000989 t 3 − 0.0486 t 2 + 0.7116 t + 1.46 ( 5 ≤ t ≤ 19 ) (1) Where, t is the ages of children in years. Formula used: Power rule of differentiation, d d x ( x n ) = n x n − 1 Theorem used: First derivative test: Equate the first derivative of an equation to 0; it gives the point of extrema (either maxima or minima ). Second derivative test: Put the point value of variable obtained by First derivative test in the second derivative of the equation, if: (a) The numeric value of second derivative comes positive, then it is a point of minima. (b) The numeric value of second derivative comes negative, then it is a point of maxima. Calculation : Differentiate equation (1) with respect to t . S ′ ( t ) = d d t ( 0.000989 t 3 − 0.0486 t 2 + 0.7116 t + 1.46 ) = d d t ( 0.000989 t 3 ) + d d t ( − 0.0486 t ) + d d t ( 0.7116 t ) + d d t ( 1.46 ) = 0.002967 t 2 − 0.0972 t + 0.7116 + 0 = 0.002967 t 2 − 0.0972 t + 0.7116 (2) Equate the above equation to 0. 0.002967 t 2 − 0.0972 t + 0.7116 = 0 The general form of a quadratic equation is, a x 2 + b x + c = 0 . The solution of above equation is given by, x = − b ± b 2 − 4 a c 2 a (3) Comparing given equation with the general form to get the values of coefficients, The value of a is 26.17332, b is − 0.0972 and c is 0.7116 . Substitute 26.17332 for a , − 0

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Chapter 4.4, Problem 67E

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Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E

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