Increasing & Decreasing Functions (Leaving Cert Mathematics): Flashcards

The tangent slopes are negative in that region.

Use the first derivative: $f'(x) < 0$.

$f'(x) = 6x - 6x^2 = 6x(1 - x)$.

Solve $x(6 - 6x) < 0$.

$f(x)$ is decreasing for $0 < x < 1$.

Show that $f'(x) > 0$ for all $x$ in its domain.

$f'(x) = 1/(1-x)^2$ using the quotient rule.

$f'(x) = 1/(1-x)^2$ for $x < 1$.

The function is increasing in its domain.

They help determine increasing or decreasing behavior.