Question

Use the information to evaluate and compare Δy and dy. (Round your answers to four decimal places.)
y = x^4 + 9 x = −3 Δx = dx = 0.01

Please Check my work, I think I'm doing this right...

Δy= f(x+ Δx)-f(x)
=f(-3+0.01)-f(-3)
=f(-2.99)-f(-3)
=4(-2.99)^3-4(-3)^3
=1.076404

dy=f^1(x)dx=f^1(-3)(0.01)=4(-.03)^3
=-1.08e^-4

Answer 1

\[
\frac{dy}{dx} = 4x^3 \\
\left[ \frac{dy}{dx} \right]_{x=-3} = 4(-3)^3 = -108\\
dy \approx = -108 * dx = -108 * 0.01 = -1.08
\]

Answer 2

thanks, i see where i went wrong

Answer 3

you are welcome.

Answer 4

\[
\Delta y = f(x+\Delta x) - f(x) = (-3+0.01)^4 + 9 - (-3)^4 - 9 = -1.0746
\]

Answer 5

so for Δy, you don't use the derivative? you just use the original function?

Answer 6

Yes. Delta y is the change in y for a small change delta x in x.

Answer 7

delta y = f(x+deltax) - f(x)