Question

Evaluate dy and Δy for f(x)=30+12x²−x³ at at x=2, and dx=Δx=0.1

Answer 1

To evaluate dy and Δy for f(x)=30+12x²−x³ at x=2, and dx=Δx=0.1, we can use calculus.

Step-by-step explanation:

To evaluate dy and Δy for f(x)=30+12x²−x³ at x=2, and dx=Δx=0.1, we can use calculus.

1. Start by finding the derivative of f(x) with respect to x: f'(x) = 24x - 3x².
2. Plug in the value of x=2 into the derivative to obtain dy: dy = f'(2) = 24(2) - 3(2²) = 48 - 12 = 36.
3. Next, multiply dy by dx to find Δy: Δy = dy*dx = 36*0.1 = 3.6.

Therefore, dy = 36 and Δy = 3.6.