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The function f (x) = -3x + 12 on R.is
- a)increasing
- b)strictly decreasing
- c)decreasing
- d)neither increasing or decreasing
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The function f (x) = -3x + 12 on R.isa)increasingb)strictly dec...
f(x) = -3x + 12
f(0) = -3(0) + 12 = 0 - 12 = 0
f(1) = 9
f(2)= 6
f(3) = 3
f(4) = 0
f(5) = -3
f(0) = -3(0) + 12 = 0 - 12 = 0
f(1) = 9
f(2)= 6
f(3) = 3
f(4) = 0
f(5) = -3
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Community Answer
The function f (x) = -3x + 12 on R.isa)increasingb)strictly dec...
Explanation:
To determine whether the given function f(x) = -3x + 12 is increasing, decreasing, or neither, we need to find the first derivative of the function and analyze its sign.
Finding the first derivative:
f(x) = -3x + 12
f'(x) = -3
Analysis of sign:
From the first derivative, we can see that it is a constant function -3, which is negative. Therefore, the sign of f'(x) is negative for all values of x in the domain R.
Conclusion:
Since the first derivative is negative for all values of x, the function f(x) is strictly decreasing on R. Therefore, the correct answer is option B, strictly decreasing.
To determine whether the given function f(x) = -3x + 12 is increasing, decreasing, or neither, we need to find the first derivative of the function and analyze its sign.
Finding the first derivative:
f(x) = -3x + 12
f'(x) = -3
Analysis of sign:
From the first derivative, we can see that it is a constant function -3, which is negative. Therefore, the sign of f'(x) is negative for all values of x in the domain R.
Conclusion:
Since the first derivative is negative for all values of x, the function f(x) is strictly decreasing on R. Therefore, the correct answer is option B, strictly decreasing.
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