Final answer:
To find the intervals where f() is negative, we need to analyze the given function f(). We can simplify the function by evaluating the exponents and performing the arithmetic operations. Only the denominator can make the expression negative, so f() will be negative for all values of ².
Step-by-step explanation:
To find the intervals where f() is negative, we need to analyze the given function f().
f() = 2 - (5²) / (2 + ²)⁴
We can simplify the function by evaluating the exponents and performing the arithmetic operations:
f() = 2 - 25 / (2 + ²)⁴
To determine the intervals where f() is negative, we need to find the values of ² that make the expression negative. Since 25 is always positive, the numerator will not affect the sign of the function. Only the denominator can make the expression negative.
The denominator (2 + ²)⁴ will be positive for all real numbers. Therefore, f() will be negative for all values of ².