math (0420) - GeoDer: stationary point

GEOMETRY OF DERIVATIVE

or

GEOMETRICAL APPLICATIONS OF CALCULUS

yay..

at point where curve slopes upwards, tangent has positive gradient and y increases as x increases, therefore f(x) increases

at point whre curve slopes downwards, tangent has negative gradient and y decreases as x increases, therefore f(x) decreases

at the turning point or stationary point, the tangent's gradient = 0 and f(x) is stationary

also, differentiation a function twice gives the concavity of the graph at that point