# Evaluate dy, if y =x^3-3x^2+7x-2 if x = 2 and dx = 0.2. Find the actual change in y if x changes...

## Question:

Evaluate {eq}dy{/eq}, if {eq}y =x^3-3x^2+7x-2{/eq} if {eq}x = 2{/eq} and {eq}dx = 0.2{/eq}. Find the actual change in {eq}y{/eq} if {eq}x{/eq} changes from {eq}x=2{/eq} to {eq}x=2.2{/eq}.

## Derivative:

We will solve the problem by differentiating the equation and then plug-in the x and dx values in the expression to get the exact change in dy.

To solve the problem we will differentiate the equation:

{eq}y=x^{3}-3x^{2}+7x-2 {/eq}

Now let us differentiate the equation:

{eq}\frac{\mathrm{d} y}{\mathrm{d} x}=3x^{2}-6+7 {/eq}

Now let us plug-in the values;

{eq}x=2\\ dx=0.2\\ dy=(7)(0.2)\\ =1.4 {/eq}