Answer:
[tex]\Delta y=0.317[/tex]
[tex]dy=0.32[/tex]
Step-by-step explanation:
To compare both expression, we recur to the formulas
[tex]\Delta y=f(x+\Delta x)-f(x)\\dy=f'(x)dx[/tex]
Replacing given values in each expression, we have:
[tex]\Delta y=f(x+\Delta x)-f(x)\\\Delta y=f(-2+0.01)-f(-2)\\\Delta y=f(-1.99)-f(-2)\\\Delta y=(-1.99)^{4}+4-(-2)^{4}-4 \\\Delta y=15.68-16=7.9601-20=0.317[/tex]
Now, to find dy, we first have to derivate the function
[tex]f(x)=x^{4} +4\\f'(x)=4x^{3}[/tex]
Then, we apply the formula
[tex]dy=f'(x)dx\\dy=4x^{3}dx\\dy=4(-2)^{3}(0.01)=32(0.01)=0.32[/tex]
Therefore, the differentials are
[tex]\Delta y=0.317[/tex]
[tex]dy=0.32[/tex]
