Question

Let y=f(x) be differentiable. below are four statements. select every true statement (there may be more that one).

A. dy = f'(x)dx
B. ∆y = f'(x+dx) - f'(x)
C. ∆y= f(x+dx) = f(x)
D. dy = f(x)dx

Answer 1

The true statements are: A. dy = f'(x)dx, B. ∆y = f'(x+dx) - f'(x), D. dy = f(x)dx. These statements represent linear approximations and changes in y based on the derivative and function values.

Step-by-step explanation:

The true statements are:

A. dy = f'(x)dx

B. ∆y = f'(x+dx) - f'(x)

D. dy = f(x)dx

Let's break down each statement:

A. dy = f'(x)dx represents a linear approximation of the change in y, given by the derivative f'(x) multiplied by dx (the change in x).

B. ∆y = f'(x+dx) - f'(x) represents the difference in the slopes at two different points x+dx and x, which gives the change in y.

D. dy = f(x)dx represents the change in y, given by the function f(x) multiplied by dx (the change in x).