Few Questions??

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For the function ff given above, determine whether the following conditions are true. Input T if the condition is ture, otherwise input F .

(a) f′(x)<0 if 0<x<2;

(b) f′(x)>0 if x>2;

(c) f′′(x)<0 if 0≤x<1;

(d) f′′(x)>0 if 1<x<4.

(e) f′′(x)<0 if x>4;

(f) Two inflection points of f(x)f(x) are, the smaller one is x=
and the other is x=

I have tried to deal with this but i get some some wrong ans. How should i determine the graph?

1 Answer
Nov 15, 2017

a) T
b) F
c) F
d) T
e) T
f) x=1 and x=4.

Explanation:

a) If f'(x)<0 it means that the function is decreasing, as you can see in the graph, the function deacrease between (0,2) and (6,∞), so it's true that it deacreases when 0<x<2.

b) If f'(x)>0 it means that the function is increasing, as you can see in the graph, the function increases between (2,6), so it's false that it increases from (2,∞) because at x=6 it starts deacrasing.

c) If f''(x)<0 it means that the function is convex, as you can seen in the graph, the function is convex between (0,1) and (4,∞), so it would be true that it's convex if it says 0<x<1 and not 0≤x<1. So it's false.

d) If f''(x)>0 it means that the function is concave, as you can seen in the graph, the function is concave between (1,4), so it's correct to say that the function is concave between (1,4).

e) If f''(x)<0 it means that the function is convex, as you can seen in the graph, the function is convex between (0,1) and (4,∞), so it's true.

f) An inflection point is the point where the function change of concave to convex or of convex to concave, so if we look we can easy identify the points x=1 and x=4 as infection points.