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The function f(x) = - 2x3 - 9x2 - 12x + 1 is an increasing function in the interval
- a)-2 < x < -1
- b)-2 < x < 1
- c)- l < x < 2
- d)1 < x < 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The function f(x) = - 2x3 - 9x2 - 12x + 1 is an increasing function in...
Given that
f(x) = - 2x3 - 9x2 - 12x + 1
- + -
- 2 - 1
implies f'(x) = - 6x2 - 18x - 12
= -6[x2 + 3x + 2]
= - 6[(x + l ) ( x + 2)]
implies f'(x) > 0, V x ∈ (-2, -1)
Hence, f(x) is increasing in the interval (-2, -1)
f(x) = - 2x3 - 9x2 - 12x + 1
- + -
- 2 - 1
implies f'(x) = - 6x2 - 18x - 12
= -6[x2 + 3x + 2]
= - 6[(x + l ) ( x + 2)]
implies f'(x) > 0, V x ∈ (-2, -1)
Hence, f(x) is increasing in the interval (-2, -1)
Most Upvoted Answer
The function f(x) = - 2x3 - 9x2 - 12x + 1 is an increasing function in...
To determine if a function is increasing or decreasing in an interval, we need to find the derivative of the function and analyze the sign of the derivative.
The derivative of f(x) = -2x^3 - 9x^2 - 12x + 1 is f'(x) = -6x^2 - 18x - 12.
To find the sign of the derivative, we can factor it as follows:
f'(x) = -6(x^2 + 3x + 2) = -6(x + 2)(x + 1).
Now, we can analyze the sign of the derivative in the given interval:
a) -2 < x="" />< />
For x = -2, we have f'(-2) = -6(-2 + 2)(-2 + 1) = 0. (The sign is not defined at this point)
For x = -1.5, we have f'(-1.5) = -6(-1.5 + 2)(-1.5 + 1) = -6(0.5)(-0.5) = 1.5 > 0. (The sign is positive)
Since the sign of the derivative changes from positive to zero (not defined) at x = -2, we can conclude that the function f(x) is increasing in the interval a) -2 < x="" />< -1.="" />
The derivative of f(x) = -2x^3 - 9x^2 - 12x + 1 is f'(x) = -6x^2 - 18x - 12.
To find the sign of the derivative, we can factor it as follows:
f'(x) = -6(x^2 + 3x + 2) = -6(x + 2)(x + 1).
Now, we can analyze the sign of the derivative in the given interval:
a) -2 < x="" />< />
For x = -2, we have f'(-2) = -6(-2 + 2)(-2 + 1) = 0. (The sign is not defined at this point)
For x = -1.5, we have f'(-1.5) = -6(-1.5 + 2)(-1.5 + 1) = -6(0.5)(-0.5) = 1.5 > 0. (The sign is positive)
Since the sign of the derivative changes from positive to zero (not defined) at x = -2, we can conclude that the function f(x) is increasing in the interval a) -2 < x="" />< -1.="" />
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Community Answer
The function f(x) = - 2x3 - 9x2 - 12x + 1 is an increasing function in...
Given that
f(x) = - 2x3 - 9x2 - 12x + 1
- + -
- 2 - 1
implies f'(x) = - 6x2 - 18x - 12
= -6[x2 + 3x + 2]
= - 6[(x + l ) ( x + 2)]
implies f'(x) > 0, V x ∈ (-2, -1)
Hence, f(x) is increasing in the interval (-2, -1)
f(x) = - 2x3 - 9x2 - 12x + 1
- + -
- 2 - 1
implies f'(x) = - 6x2 - 18x - 12
= -6[x2 + 3x + 2]
= - 6[(x + l ) ( x + 2)]
implies f'(x) > 0, V x ∈ (-2, -1)
Hence, f(x) is increasing in the interval (-2, -1)
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