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

The derivative $f'(x)$ represents the slope of $f(x)$.

$f'(x) > 0$ indicates $f(x)$ is increasing.

$f'(x) < 0$ indicates $f(x)$ is decreasing.

At a stationary point, $f'(x) = 0$.

$f'(x)$ crosses $x$-axis from positive to negative.

$f'(x)$ crosses $x$-axis from negative to positive.

$f'(x)$ is increasing if $f(x)$ is concave up.

$f'(x)$ is decreasing if $f(x)$ is concave down.

$f'(x)$ crosses $x$-axis at each stationary point of $f(x)$.

Look for sign changes and smoothness in the curve.