Question

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?

Answer 1

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.