# Few Questions??

## 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?

Nov 15, 2017

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

#### Explanation:

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

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

c) If $f ' ' \left(x\right) < 0$ it means that the function is convex, as you can seen in the graph, the function is convex between $\left(0 , 1\right)$ 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 $f ' ' \left(x\right) > 0$ it means that the function is concave, as you can seen in the graph, the function is concave between $\left(1 , 4\right)$, so it's correct to say that the function is concave between $\left(1 , 4\right)$.

e) If $f ' ' \left(x\right) < 0$ it means that the function is convex, as you can seen in the graph, the function is convex between $\left(0 , 1\right)$ 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.