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char808
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Homework Statement
Finding the linearization of the function F(t) = t2 /2 + 2t at t = -1.
Homework Equations
F'(t) = t+2
The Attempt at a Solution
F(t) + F'(t)(t-a)
-3+1(t+1) = t -2
The linearization of a function is the process of approximating a nonlinear function with a linear function. This is done by finding the tangent line to the function at a given point, which serves as an approximation of the function near that point.
Linearization is useful because it allows us to approximate complicated functions with simpler, linear functions. This makes it easier to analyze and understand the behavior of the function, especially near a specific point.
The linearization of a function is calculated by finding the derivative of the function at a given point, and then using that derivative to find the equation of the tangent line at that point.
The equation for the linearization of function F(t) = t2 /2 + 2t is y = t + 2. This is because the derivative of the function is y' = t + 2, and the equation of the tangent line is y = y'x + b, where b is the y-intercept (in this case, b = 2).
The accuracy of the linearization of a function depends on the point at which it is being approximated and the behavior of the function around that point. Generally, the closer the point is to the point of tangency, the more accurate the linearization will be.