Graphical Behaviour of Functions (HSC SSCE Mathematics Advanced): Flashcards

Gradient of tangent line to curve $y = f(x)$ at point $x$

When $f'(x) > 0$

When $f'(x) < 0$

$f'(x) = 0$

$f(x) = ax^3 + bx^2 + cx + d$ where $a \neq 0$

Set derivative equal to zero and solve for $x$

Become $x$-intercepts

One less than original function

$f'(c) \approx \frac{f(c + h) - f(c)}{h}$

Smaller