Increasing & Decreasing Functions (Edexcel A-Level Mathematics): Quizzes

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Increasing & Decreasing Functions
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For f(x)f(x) to be increasing on interval II with x1<x2x_1 < x_2, what must be true?

f(x1)≤f(x2)f(x_1) \leq f(x_2)

If f′(x)>0f'(x) > 0 for all xx in an interval, what can we conclude about f(x)f(x)?

f(x)f(x) is increasing on that interval

If f′(x)<0f'(x) < 0 for all xx in an interval, what is true about f(x)f(x)?

f(x)f(x) is decreasing on that interval

Where do critical points occur?

Where f′(x)f'(x) is zero or undefined

If f′(x)=0f'(x) = 0 for all xx in an interval, what is the function?

Constant on that interval

After finding critical points, what do we determine in each interval?

The sign of the derivative

What is the first step in finding intervals of increase and decrease?

Calculate the first derivative f′(x)f'(x)

For f(x)=x3−3x2+2f(x) = x^3 - 3x^2 + 2, what are the critical points?

x=0x = 0 and x=2x = 2

For f(x)=1xf(x) = \frac{1}{x}, why is the function decreasing everywhere?

f′(x)=−1x2f'(x) = -\frac{1}{x^2} is always negative

Which is an application of increasing and decreasing functions?

Finding maximum or minimum values

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