Find the values of x for which the derivative is negative of the function f (x) = 1-x / x ^ 2 + 8 are negative.
| August 22, 2021 | education
f (x) = (1 – x) / (x ^ 2 + 8);
Find the value of x if the derivative <0;
Derivative f (x) = f ‘(x) = ((1 – x) / (x ^ 2 + 8))’ = ((1 – x) ‘* (x ^ 2 + 8) – (x ^ 2 + 8) ‘* (1 – x)) / (x ^ 2 + 8) ^ 2 = (- (x ^ 2 + 8) – 2 * x * (1 – x)) / (x ^ 2 + 8) ^ 2 = (- x ^ 2 – 8 – 2 * x * + 2 * x ^ 2)) / (x ^ 2 + 8) ^ 2 = (x ^ 2 – 2 * x – 8)) / (x ^ 2 + 8) ^ 2;
(x ^ 2 – 2 * x – 8)) / (x ^ 2 + 8) ^ 2 <0;
x ^ 2 – 2 * x – 8 <0;
x = – 2 and x = 4;
Answer: – 2 <x <4.
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