F(x) = =
Find f'(x) and f''(x).
+
EL
ALEHER
24
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f''(x) = {
Epe

To make things easier, first rewrite

f(x) = x / (x + 7/x) = x ² / (x ² + 7)

i.e. multiply f by x/x, which is valid because x can't be 0 anyway as it's outside the domain of f.

Now, by the quotient and chain rules, we get

f '(x) = ((x ² + 7) (x ²)' - x ² (x ² + 7)') / (x ² + 7)²

… = (2x (x ² + 7) - x ² (2x)) / (x ² + 7)²

… = (2x ³ + 14x - 2x ³) / (x ² + 7)²

… = 14x / (x ² + 7)²

f ''(x) = ((x ² + 7)² (14x)' - (14x) ((x ² + 7)²)') / ((x ² + 7)²)²

… = (14 (x ² + 7)² - (14x) (2 (x ² + 7)² (x ² + 7)')) / (x ² + 7)⁴

… = (14 (x ² + 7)² - (14x) (2 (2x) (x ² + 7)²)) / (x ² + 7)⁴

… = (14 (x ² + 7)² - 4x (14x) (x ² + 7)²) / (x ² + 7)⁴

… = 14 (x ² + 7)² (1 - 4x) / (x ² + 7)⁴

… = 14 (1 - 4x) / (x ² + 7)²

… = (14 - 56x) / (x ² + 7)²

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )