First Principles for Derivatives (HSC SSCE Mathematics Advanced): Flashcards

Instantaneous rate of change of function

Gradient of tangent line to curve at a point

$\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

Value gradient approaches as interval approaches zero

Tangent line

$\frac{f(x+h) - f(x)}{h}$

Factorise $h$ from the numerator

After cancelling $h$, not before

Substitute the $x$-value into $f'(x)$

$x^2 + 2xh + h^2$