Finding the Values of x for Increasing Functions: A Simple Q&A

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to cut it short, was asked to find the values of x for which f(x) is an increasing function
$$\dfrac{(x^2 + 3)}{4x + 1} = f(x)$$
$$\dfrac{(4x-6)(x+2)}{(4x+1)^2} = f'(x)$$ so setting this to be greater than zero I get the values of x < -2, and x > 2/3 however in the answers they got x <= -2 and x >= 2/3, and they set f'(x) to be >= 0. I thought with increasing functions f'(x) is > 0?

 

[Mark44]

to cut it short, was asked to find the values of x for which f(x) is an increasing function
$$\dfrac{(x^2 + 3)}{4x + 1} = f(x)$$
$$\dfrac{(4x-6)(x+2)}{(4x+1)^2} = f'(x)$$ so setting this to be greater than zero I get the values of x < -2, and x > 2/3 however in the answers they got x <= -2 and x >= 2/3, and they set f'(x) to be >= 0. I thought with increasing functions f'(x) is > 0?

Some texts distinguish between increasing and strictly increasing. For an increasing function, if a < b, then f(a) ≤ f(b). For a function that is strictly increasing, if a < b, then f(a) < f(b).

And similar for decreasing/strictly decreasing.

 

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Some texts distinguish between increasing and strictly increasing. For an increasing function, if a < b, then f(a) ≤ f(b). For a function that is strictly increasing, if a < b, then f(a) < f(b).

And similar for decreasing/strictly decreasing.

oh I see, thank you!