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Match slope and concavity intervals on a cubic graph

Using the given graph of y=0.1x(x−6)(x+6)y=0.1x(x-6)(x+6), match (a) strictly increasing, (b) strictly decreasing, (c) concave upwards and (d) concave downwards to the printed sets: {x∈R:−3.46<x<3.46}\{x\in\mathbb R:-3.46<x<3.46\}; {x∈R:x<0}\{x\in\mathbb R:x<0\}; {x∈R:x>0}\{x\in\mathbb R:x>0\}; {x∈R:x<−3.46 or x>3.46}\{x\in\mathbb R:x<-3.46\text{ or }x>3.46\}.

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Graph of 0.1x(x−6)(x+6), roots −6,0,6, printed approximate turning labels (−3.46,8.31),(3.46,−8.31). Concavity changes at 0; turning abscissae exact ±2sqrt3.
Graph of 0.1x(x−6)(x+6), roots −6,0,6, printed approximate turning labels (−3.46,8.31),(3.46,−8.31). Concavity changes at 0; turning abscissae exact ±2sqrt3.
Graph of 0.1x(x−6)(x+6), roots −6,0,6, printed approximate turning labels (−3.46,8.31),(3.46,−8.31). Concavity changes at 0; turning abscissae exact ±2sqrt3.

CJC · Lecture · Example 4

Identify whether the given curve is a function, an implicit relation or a derivative graph before choosing the test.

Read the worked solution