Let f(x)= -6x^2+3x+10f(x)=−6x2+3x+10 then choose the set of correct options regarding f(x)f(x)
Answers
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Given: f( x ) = − 6x² + 3 x + 10
To Find : correct options
https://brainly.in/question/47399766 for options
• If x ∈ [ 2 , 3 ] ∪ ( 5 , ∞ ) , then f ( x ) is positive.
•The slope of the parabola f ( x ) is − 12 x + 3
• If x ∈ [ 0 , 1 ] ∩ [ 0.5 , ∞ ) , then f ( x ) is negative.
• The slope of the parabola f ( x ) is − 6 x + 3
• The vertex of the parabola f ( x ) is at x = 1 /4
Solution:
f( x ) = − 6x² + 3 x + 10
f'(x) = -12x + 3
Hence The slope of the parabola f ( x ) is − 12 x + 3 is CORRECT
The slope of the parabola f ( x ) is − 6 x + 3 is INCORRECT
f( x ) = − 6x² + 3 x + 10
= -6(x² - x/2 ) + 10
= -6(x² - x/2 + (1/4)²) + 6(1/16) + 10
= -6 (x - 1/4)² + 83/8
Vertex is ( 1/4 , 83/8)
The vertex of the parabola f ( x ) is at x = 1 /4 is CORRECT
− 6x² + 3 x + 10
x ∈ [ 2 , 3 ] ∪ ( 5 , ∞ ) , then f ( x ) is positive.
check for 2
=> -24 + 6 + 10 = -8 < 0
Hence INCORRECT
If x ∈ [ 0 , 1 ] ∩ [ 0.5 , ∞ ) , then f ( x ) is negative.
x ∈ [ 0 , 1 ] ∩ [ 0.5 , ∞ )
=> x ∈ [ 0.5 , 1 ]
x = 1 => f(x) = 7
Hence INCORRECT
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