Using Linearization to Approximate Function Values We will create a linearization to approximate the value of V12. To create the linearization you will need the first derivative of the function f(x) = Vx and to What is f(9) ? What piece of information does this value give you as you create your tangent line? judge whether your approximation is an over- or under- estimate, you will need the second derivative. These derivatives are: f'(x) = 1 2vx f"(x) = -1 16x3 %3D What is f'(9) ? What piece of information does this value give you as you create your tangent line? A number that is close to 12 whose square root is easy to calculate is 9. We will create our linearization of f at x= 9. To start the process we must build our tangent line at x = 9 , which means we need to know the coordinates of the point of tangency at x = 9 and the slope of the tangent line. Submit

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.