Explanation Given: The given problem is h ( u ) = 1 u ( u + 9 ) . Concept Used: The tangent line of a curve will be horizontal when d y / d x = 0 , because the derivative measures the slope and slope of a horizontal line is 0. Power rule of differentiation formula d d x x n = n x n − 1 Calculation: To find the coordinates of point(s) on the graph of function h ( u ) = 1 u ( u + 9 ) where the tangent line is horizontal, we need to find the points where derivative of the function is 0. Now, to find derivative of f differentiate both side of the equation with respect to x as h ( u ) = 1 u ( u + 9 ) d h ( u ) d u = d d u [ ( u u + 9 u ) ] = d d u [ u u − 1 / 2 + 9 u − 1 / 2 ] = d d u [ u 1 − 1 / 2 + 9 u − 1 / 2 ] = d d u [ u 1 / 2 + 9 u − 1 / 2 ] = d<

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 3.2, Problem 37PS

To determine

To find the coordinates of point(s) on the graph of given function h(u)=1u(u+9) where the tangent line is horizontal.

Expert Solution & Answer

Chapter 3 Solutions

Calculus

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To find the coordinates of point(s) on the graph of given function h ( u ) = 1 u ( u + 9 ) where the tangent line is horizontal.

Solution Summary: The author explains that to find the coordinates of point(s) on the graph of function h(u)=1sqrt

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To find the coordinates of point(s) on the graph of given function h(u)=1u(u+9) where the tangent line is horizontal.

Chapter 3 Solutions