Find the linearization L(x) of the function at a.f(x) = x4 + 2x2, a = −1
Question
Find the linearization L(x) of the function at a.f(x) = x4 + 2x2, a = −1
Solution
The linearization of a function at a point a is given by the formula:
L(x) = f(a) + f'(a)(x - a)
Here, f(x) = x^4 + 2x^2.
First, we need to find the derivative of f(x), f'(x):
f'(x) = 4x^3 + 4x.
Now, we can substitute a = -1 into f(x) and f'(x) to find f(a) and f'(a):
f(-1) = (-1)^4 + 2*(-1)^2 = 1 + 2 = 3, f'(-1) = 4*(-1)^3 + 4*(-1) = -4 - 4 = -8.
Finally, we can substitute these values into the formula for L(x):
L(x) = f(-1) + f'(-1)(x - (-1)) = 3 - 8(x + 1).
So, the linearization L(x) of the function at a = -1 is L(x) = 3 - 8(x + 1).
Similar Questions
Find the linearization L(x) of the function at a.f(x) = x3/4, a = 16
Find the linearization L(x) of the function at a.f(x) = cos(x), a = 3𝜋/2
Find the linearization L(x) of the function at a.f(x) = sin(x), a = 𝜋3
Find the linearization L(x,y) of the function f(x, y) = (x + y + 2)2 at the point (1, 2)
The function L is a linear transformation function of vectors given by L(v) = Av , where20 A = 1 −1and av = a b, = b. Which of the following is the image of −2, 3 under the linear transformation L ?(A) 1, −3(B) −4, −5(C) −4, −3(D) −4, 0
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.