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Decreasing functions
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Skybird
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WIth a decreasing function the gradient is negative in some interval. Let's say we have
(3x - 1)(x+3 ) < 0
So x is either 1/3 or -3. How can you tell whether the gradient is -ve or +ve around these values of x without substituting a value just left or right of the x value into the derivative ?
(3x - 1)(x+3 ) < 0
So x is either 1/3 or -3. How can you tell whether the gradient is -ve or +ve around these values of x without substituting a value just left or right of the x value into the derivative ?
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Pangol
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(Original post by Skybird)
WIth a decreasing function the gradient is negative in some interval. Let's say we have
(3x - 1)(x+3 ) < 0
So x is either 1/3 or -3. How can you tell whether the gradient is -ve or +ve around these values of x without substituting a value just left or right of the x value into the derivative ?
WIth a decreasing function the gradient is negative in some interval. Let's say we have
(3x - 1)(x+3 ) < 0
So x is either 1/3 or -3. How can you tell whether the gradient is -ve or +ve around these values of x without substituting a value just left or right of the x value into the derivative ?
In this case, your gradient is a quadratic, so this is solving a quadratic inequality. You probably know that the gradient is either going to be negative between th critical values you have found or "outside" them. So pick a value between them (0 is the obvious candidate) and see what you get. If negative, it's between them, if not, it's outside them.
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