Question

The function f(x) changes value when x changes from x_{0} to x_{0}+d x . f(x)=4 x²-5 x-3, x_{0}=-2, d x=0.1

Find the change δ f=f \ (x_{0}+d x-f

Answer 1

The change in the function f(x) when x changes from x0 to x0+dx is calculated by substituting the values into the function and subtracting the results. In this case, with f(x) = 4x^2 - 5x - 3, x0 = -2, and dx = 0.1, the change in f(x) is 21.47.

Step-by-step explanation:

To find the change in the function f(x) when x changes from x0 to x0+dx, we can substitute the values into the function and subtract.

Given that f(x) = 4x^2 - 5x - 3, x0 = -2, and dx = 0.1, we can calculate:

f(x0+dx) - f(x0) = f(-2+0.1) - f(-2)

Substituting the values and evaluating, we get:

f(-1.9) - f(-2) = 4(-1.9)^2 - 5(-1.9) - 3 - (4(-2)^2 - 5(-2) - 3)

= 10.47 - (-11)

= 21.47

Therefore, the change in f(x) is 21.47.