# Maths - Sketching Gradient Functions

> Source: https://ollybritton.com/notes/a-level/maths/topics/sketching-gradient-functions/ · Updated: 2021-01-27 · Tags: maths, differentiation

## See Also
- [Maths - Differentiation](https://ollybritton.com/notes/a-level/maths/topics/differentiation/)

## Flashcards
##### Visually, if $y = f(x)$ is a maximum or minimum, what does the curve $y = f'(x)$ do??
Cuts the $x$-axis.

##### Visually, if $y = f(x)$ is a point of inflection, what does the curve $y = f'(x)$ do??
Touches the $x$-axis.

##### Visually, if $y = f(x)$ has a positive gradient, where is the curve $y = f'(x)$??
Above the $x$-axis.

##### Visually, if $y = f(x)$ has a negative gradient, where is the curve $y = f'(x)$??
Below the $x$-axis.

##### Visually, if $y = f(x)$ has a vertical asymptote, what happens to the curve $y = f'(x)$??
It also has a vertical asymtote.

##### Visually, if $y = f(x)$ has a horizontal asymptote, what happens to the curve $y = f'(x)$??
It has a horizontal asymptote at the $x$-axis.

##### When sketching a gradient function from the graph of the normal function, what should you do first??
Add the stationary points.

##### After you've added the stationary points to a sketch of a gradient function, what should do next??
Don't sketch it, move along the graph and plot approximate points.

##### ![PHOTO EXAMPLE FUNCTION FOR SKETCHING](example-function-for-sketching.png) Should the gradient function on the left side of the graph be higher or lower than on the right side??
Lower.

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