Is a point of inflection concave or convex? - Which answer is correct?

AI Thread Summary
A point of inflection does not necessarily require the existence of an inflection point if the function has undefined areas. The discussion emphasizes the importance of analyzing the second derivative to determine concavity or convexity in different intervals. Some participants express frustration over the complexity of identifying these points, leading to confusion. It is highlighted that spending excessive time on such problems without clear solutions can be unproductive. Understanding the behavior of the second derivative is crucial for accurately determining concavity and convexity.
Sarah66
Messages
1
Reaction score
0
Homework Statement
Hello everybody, :)
I have a problem with determining the intervals of convexity and concavity of this function:
Relevant Equations
there are no inflection points here for me
problem1.png

but for me there is no solution to this inequality...
I never wait for a ready answer but I've already spent 4 hours on it and I still don't know what to mark...
 
Physics news on Phys.org
Sarah66 said:
there are no inflection points here for me
There doesn’t need to be an inflection point to switch between concave and convex if there are points where the function is undefined.
 
Check the sign of the 2nd derivative on each interval if you aren't sure.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
Back
Top