For a function f(x), the difference quotient is 21x2 + 21xh + 7h2 + 2. Which statement describes how to determine the average ra

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For a function f(x), the difference quotient is 21x2 + 21xh + 7h2 + 2. Which statement describes how to determine the average ra

te of change of f(x) from x = –3 to x = 2? Substitute –3 for x and 2 for h in the difference quotient. Substitute –3 for x and 5 for h in the difference quotient. Substitute 2 for x and –3 for h in the difference quotient. Substitute 2 for x and –5 for h in the difference quotient.

Mathematics

1 answer:

aleksley [76] · Answer 1 · 2021-12-02T04:09:27+03:00

Answer:

Substitute –3 for x and 5 for h in the difference quotient.

Step-by-step explanation:

The difference quotient for the function f(x) is 21x² + 21xh + 7h² + 2. Now, we know that the difference quotient equal f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. The change in x is h = x₂ - x₁. So, if x changes from x = -3 to x = 2, where x₁ = -3 and x₂ = 2, h = x₂ - x₁ = 2 - (-3) = 2 + 3 = 5.

So to find the average rate of change of f(x) from x = -3 to x = 2, we substitute x = -3 and h = 5 into the difference equation f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. Since, x starts at x = -3 and increases by 5 units to x = 2.