Let be defined by

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f:\mathbb R \to \mathbb R

be defined by

f(x)=x^{3}-6x+2

. Answer the following. (i) Draw a rough but clearly labelled sketch of the curve

y=f(x)

showing all intercepts and turning points. (ii) From your sketch, decide whether

f

is one–one on

\mathbb R

. Give a brief justification based on the appearance of the graph. (iii) Write the intervals on which

f

is strictly increasing and hence one–one.