Answer:
f(x + h) = 3x³ + x² + 9h²x + 3h³ + h² + 9hx² + 2hx
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Distributive Property
- Expand by FOIL (First Outside Inside Last)
- Combining like terms
Step-by-step explanation:
<u>Step 1: Define function</u>
f(x) = x² + 3x³
f(x + h) is x = x + h
<u>Step 2: Simplify</u>
- Substitute: f(x + h) = (x + h)² + 3(x + h)³
- Expand by FOILing: f(x + h) = (x² + 2hx + h²) + 3(x + h)³
- Rewrite: f(x + h) = (x² + 2hx + h²) + 3(x + h)²(x + h)
- Expand by FOILing: f(x + h) = (x²+2hx+h²) + 3(x² + 2hx + h²)(x+h)
- Distribute/Expand: f(x + h) = (x²+2hx+h²) + 3(x³+3hx²+3h²x+h³)
- Distribute 3: f(x + h) = (x²+2hx+h²)+(3x³+9hx²+9h²x+3h³)
- Combine like terms: f(x + h) = 3x³+x²+9h²x+3h³+h²+9hx²+2hx
Answer:180
Step-by-step explanation:
9514 1404 393
Answer:
ACBD-BDAC
Step-by-step explanation:
It is convenient to compare the values of each of the functions when h=1. On the graphs, find 1 on the horizontal axis, then read the value of the function at that point from the vertical axis.
For the equations, the value for h=1 will be its coefficient in the equation.
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1) a: 80,b: 50, c: 75, d: 30
Fastest to slowest is ACBD.
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2) a: 4, b: 2, c: 8, d: 3
Slowest to fastest is BDAC
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The code is these lists, separated by a dash: ACBD-BDAC.
