Question

Use the information to evaluate and compare Δy and dy. (Round your answers to four decimal places.)

Answer 1

Answer:

$\Delta y=0.317$

$dy=0.32$

Step-by-step explanation:

To compare both expression, we recur to the formulas

$\Delta y=f(x+\Delta x)-f(x)\\dy=f'(x)dx$

Replacing given values in each expression, we have:

$\Delta y=f(x+\Delta x)-f(x)\\\Delta y=f(-2+0.01)-f(-2)\\\Delta y=f(-1.99)-f(-2)\\\Delta y=(-1.99)^{4}+4-(-2)^{4}-4 \\\Delta y=15.68-16=7.9601-20=0.317$

Now, to find dy, we first have to derivate the function

$f(x)=x^{4} +4\\f'(x)=4x^{3}$

Then, we apply the formula

$dy=f'(x)dx\\dy=4x^{3}dx\\dy=4(-2)^{3}(0.01)=32(0.01)=0.32$

Therefore, the differentials are

$\Delta y=0.317$

$dy=0.32$

Answer 2

Y'=4x^3+4
(f(x+dx)-f(x))/dx
f(-2+.01)-f(-2)/.01
((15.6824+f(x))/.01
23.6824/.01=2368.2392