Maths - Sketching Gradient Functions
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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.
Should the gradient function on the left side of the graph be higher or lower than on the right side?
Should the gradient function on the left side of the graph be higher or lower than on the right side?Lower.