Find the linearization L (x) of the function f (x) = 4 x^2 + 7 x at the point x = 1 and use it to estimate the value of f (12 / 10). Find the linearization L(x) to the function f(x) = 5x^{-2} at the poin...
Evaluate g (x) = ln x at the given value of x without using a calculator. x = e^{-4} Let f(x) = (x - 1)^2, g(x) = e^{- 2x}, and h(x) = 1 + \ln(1 - 2x). a) Find the linearizations of f, g, and h at a = 0. ...
In this lesson, learn what critical numbers of functions are and how to find the critical points of a function. Moreover, see examples of critical...
Let f(x) = (x - 1)^2, g(x) = e^{-2x} and h(x) = 1 + \ln (1 - 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened? (b) Graph ...
The equation for finding a, b, and k is derived from the general form of a logarithmic function, y = a + b ln(x), where x represents time and y represents temperature. By taking the logarithm of both sides and using a technique called linearization, we can transform the equation into...
For a differentiable function f, a solution of the equation f(x)=0 may be approximated by the Newton's Method which, for a starting point x0 proposes to look the next (approximation) x1 to be the x-intercept of the tangent line to the grap...