Convex and Concave Curves

[MatteoDobrich]

Hello,
I'm having a hard time figuring which is the correct way of approaching to the following question:

For each of the following intervals, determine whether y=x^5-2x^4-3x+2 is concave over the whole interval, convex over the whole interval, or has a point of inflection in the interval:
a) -1<x<0
b) 0<x<1
c) 1<X<2
d) 2<x<3

Kind regards
Matteo

 

[Deleted member 4993]

Hello,
I'm having a hard time figuring which is the correct way of approaching to the following question:

For each of the following intervals, determine whether y=x^5-2x^4-3x+2 is concave over the whole interval, convex over the whole interval, or has a point of inflection in the interval:
a) -1<x<0
b) 0<x<1
c) 1<X<2
d) 2<x<3

Kind regards
Matteo

What are the mathematical characteristics of concave line & convex line & point of inflection ?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem.

 

[BigBeachBanana]

 

[MatteoDobrich]

What are the mathematical characteristics of concave line & convex line & point of inflection ?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Hi,
I tried to solve the exercise by posing f"(x)>0 then, <0 and finally =0 and then compare the results with the intervals. But, for example, with f"(x)>0 I would have 20^3-24^2>0 which gives me x>6/5 and as I interpreted it I assumed that intervals c) and d) had a concave curve.
Is my reasoning right or do I have to approach this problem differently?

kind regards
matteo

 

[Deleted member 4993]

y=x^5-2x^4-3x+2

y" = 20*x^3 - 24*x^2 = 4*x^2 * (5x - 6)

so y" =0 at x = 0 and x = 6/5 = 1.2

for -1<x<0

x" < 0 in the whole region - so what is the conclusion for this region

Region (c) straddles an inflection point - so it changes curvature within the interval.

I would analyze at every region like above.

finish it....