Question

A railway track has the form of a curvey. where x and y are expressed in
miles. At what rate will the engine be changing direction with respect to the
distance when passing through the point (1.1)?​

Answer 1

Answer:

rate of change of Curves is Given as Derivative of the Curve.

for example : if the Curve is y=x^2 , then Rate of change is 2x

another example if Cyrve is a. Circle then rate of change depends on both x,y and is given as

dy/dx =-x/y

so you get how much Y changes for a small change in x for a Given x,y

hope you found it useful.

Answer 2

Concept:

The rate at which one quantity changes in relation to another is known as the derivative. The rate of change of a function is described mathematically as dy/dx = f(x) = y'.

Derivatives have been employed on both a small and large scale. The idea of derivatives is applied in a variety of contexts, such as the rate at which an object's size and form vary or how temperature changes, etc.

Rate of a Quantity's Change

The broadest and most significant use of derivative is this. For instance, we may use the derivative form dy/dx to determine the rate of change of a cube's volume with respect to its decreasing sides. dy stands for the rate of change of volume

Given:

A railway track has the form of a curvey. where x and y are expressed in

miles

Find:

At what rate will the engine be changing direction with respect to the

distance when passing through the point (1.1)?​

Solution:

Let the curve be y(x)

rate of change of Curves is Given as Derivative of the Curve.

So, rateof change of curve=y'(x)

Rate of change of curve at(1,1)=y'(1)

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