find dy for the given values of x and δx. y = 2x³ - 6x; x = - 3 and δx = 0.1 dy = (round to the nearest…
find dy for the given values of x and δx. y = 2x³ - 6x; x = - 3 and δx = 0.1 dy = (round to the nearest tenth as needed.)
Answer
Explanation:
Step1: Find the derivative of y
The derivative of $y = 2x^{3}-6x$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $y^\prime=\frac{dy}{dx}=6x^{2}-6$.
Step2: Evaluate the derivative at x = - 3
Substitute $x=-3$ into $y^\prime$: $y^\prime(-3)=6(-3)^{2}-6=6\times9 - 6=54 - 6 = 48$.
Step3: Use the differential formula
The differential formula is $dy=y^\prime(x)\Delta x$. We know $y^\prime(-3) = 48$ and $\Delta x=0.1$. So $dy=48\times0.1$.
Answer:
$4.8$