Sketching Gradient Functions (Edexcel A-Level Mathematics): Quizzes

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Sketching Gradient Functions
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Where does f′(x)f'(x) lie when f(x)f(x) is increasing?

Above the xx-axis

How does f′(x)f'(x) cross the xx-axis at a local maximum of f(x)f(x)?

From positive to negative

What is the value of f′(x)f'(x) at a stationary point of f(x)f(x)?

f′(x)=0f'(x) = 0

Where does f′(x)f'(x) lie when f(x)f(x) is decreasing?

Below the xx-axis

What happens to f′(x)f'(x) when f(x)f(x) is concave up?

f′(x)f'(x) is increasing

How does f′(x)f'(x) cross the xx-axis at a local minimum of f(x)f(x)?

From negative to positive

What does f′(x)f'(x) do at an inflection point of f(x)f(x)?

Reaches a max/min, not crossing axis

What happens to f′(x)f'(x) when f(x)f(x) is concave down?

f′(x)f'(x) is decreasing

What do sign changes in f′(x)f'(x) indicate about f(x)f(x)?

Transitions between inc/dec behaviour

How should the gradient function f′(x)f'(x) be sketched?

As a smooth curve without sharp corners

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