max Min point on a graph
Features of a curve of functions Video
Displacement,Velocity acceleration . school typr problem
Concavity
Answer the following questions based on above :
1.How do you identify the derivative signs at different points on the graph?
2.What features of the slope defines that the curve at a point region is concave down/concave up (cup up/cup down)?
3.What is an inflection point.Where does an inflection point occur in a graph? What is the difference between the slope '0' point (also known as stationary point) and an inflection point.
4.Does the concavity always alternate like up/down in general or can there be exceptions ?If exceptions are there -them what are they?
Inflection point testing Video tells you some techniques of analysing.
Answer the following.
The video showed a quick way to analyse slopes using signs without drawing the derivative graph.,what was it.Give example.
A note on linkin 1st derivative fraph to f(x)
f '(x) - to 0 to+ U [smiling f(x) ] ;f'(x) + 0 - ∩ (Sad f (x))
It also showed how to look for concavity using signs of 2nd derivative and the inflection point..describe it.
When can there be no inflection point?
Exercise:
1.Graph the following f(x), fulfilling all conditions:
Domain [-3,3],f(-3)=4,f(3)=1
f(x) increasing on [-3,-1],f(x) decreasing on [-1,1],f’’(x)>0 on [-1,1],f”(x)<0 on [1,3].
Find Abs Max and Min points and inflection points.
State with reasons
2. y=-x^3=3x^2+1 .at which point is the slope Maximum.
2. y=-x^3=3x^2+1 .at which point is the slope Maximum.
Learning CapsculeBahskara Academy link
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