Answer:
f(x) is concave up whenever:
B. 3x²−10 is positive
f(x) is concave down whenever:
A. 3x²−10 is negative
The points of inflection of f(x) are the same as:
B. the zeros of 3x²−10
Step-by-step explanation:
Given the function f(x) = 1 / (x²+10)
We can determine the concavity by finding the second derivative.
If
f"(x) > 0 ⇒ f(x) is concave up
If
f"(x) < 0 ⇒ f(x) is concave down
Then
f'(x) = (1 / (x²+10))' = -2x / (x²+10)²
⇒ f"(x) = -2*(10-3x²) / (x²+10)³
if f"(x) = 0 ⇒ -2*(10-3x²) = 0 ⇒ 3x²-10 = 0
f(x) is concave up whenever 3x²−10 > 0
f(x) is concave down whenever 3x²−10 < 0
The points of inflection of f(x) are the same as the zeros of 3x²-10
it means that 3x²-10 = 0
If you multiply a negative number by a positive number, you get a negative product. if you were to multiply two positive or two negative numbers, you'd get positive products.
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Since
, and you have a corresponding term in the given Riemann sum of
, you know the integral is being taken over an interval of length 5, so you can omit the second choice.
Next,
corresponds to
with
. The fact that
alone tells you that the interval of integration starts at 3, and since we know the interval has length 5, that leaves the first choice as the correct answer.
Answer:1 page
Step-by-step explanation:
Divide
