Let y = 3x² + 2. If x changes from 10 to 10.1, then what is the total change in y?

Concept:

Let small charge in x be Δx and the corresponding change in y is Δy.

Therefore \(\rm \Delta y = \rm \frac{dy}{dx}\Delta x\)

Calculation:

Given: y = 3x² + 2

To Find: total change in y = Δy

x changes from 10 to 10.1

So, Δx = 10.1 - 10 = 0.1

Now, y = 3x² + 2

Differentiating with respect to x, we get

\(\Rightarrow \rm \frac{dy}{dx} = 6x\)

As we know, \(\rm \Delta y = \rm \frac{dy}{dx}\Delta x\)

\(\Rightarrow \rm \Delta y = \rm 6x\Delta x\)

Put x = 10 and Δx = 0.1

\(\therefore \rm \Delta y = \rm 6\times 10\times 0.1 = 6\approx 6.03\)