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How do I 'prove f(x) is an increasing function'? Watch

1. We've only had 2 weeks to learn Core 2, so there's a lot that we haven't been taught. Like, for example, what does 'prime' mean in the context of f'(x) - it's the same as dy/dx right?

Anyway, I'm not sure how to prove that 'f is an increasing function'. The specific question I'm stuck on is pictured below (question 10.b.ii).

Thanks for any input.
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2. (Original post by JRChapman)
We've only had 2 weeks to learn Core 2, so there's a lot that we haven't been taught. Like, for example, what does 'prime' mean in the context of f'(x) - it's the same as dy/dx right?

Anyway, I'm not sure how to prove that 'f is an increasing function'. The specific question I'm stuck on is pictured below (question 10.b.ii).

Thanks for any input.
The prime is the '. Yes it means dy/dx where y = f(x)
To show that it is an increasing function prove the gradient is greater than 0.
3. If then the function is increasing.
4. an increasing function always has a positive gradient for all real x.
the prime symbol is the apostrophe in f'(x) which is the first derivative of f(x)
5. From the derivative, you should be able to show that all values of x result in a positive dy/dx.

And if dy/dx > 0,
The gradient is always positive and therefore function is always increasing.

Hope that helps!

Posted from TSR Mobile
6. Increasing Function means the parts of the graph where the gradient is positive (bigger than 0). You have to use f'(x) to find those parts.

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Updated: April 12, 2013
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