Graphs and their Derivatives Help!!!! (1 Viewer)

[noobonastick]

Hi im really confused with this stuff, please help
This is the worksheet im currently doing.




sorry its a bit big, and basically i am confused about what second derivative and first derivative measures.

say for Question 2v , where is it negative? (i have the answers but don't know how to arrive at them)

i also dont understand Q3ii and Q3 iii

for question 4, f'(6) = 2, i dont know what this means.. and also i dont get Q4iv

and i dont understand q5 and q6ii and q6iii

Sorry, i have so many questions, but i need help, i have a test in 2 days... =[.

 

[clintmyster]

first derivative is the gradient of a curve. Equating it to 0 can give you turning points. The second derivative is useful in determining points of inflection.

f(6) means when y = 6 and f'(6) means when derivative has a value of 6
zeroes are where the curve cuts or touches the x axis

 

[Timothy.Siu]

i think 2v is from d<x<h
u shud read over the basics first, understand the concepts first.
if u dont know this ur in trouble....
read over the explanations of derivatives and wat they mean and do.

 

[noobonastick]

first derivative is the gradient of a curve. Equating it to 0 can give you turning points. The second derivative is useful in determining points of inflection.

yes i know this..

f(6) means when y = 6 and f'(6) means when derivative has a value of 6 zeroes are where the curve cuts or touches the x axis

i dont get it..., what does f'(2) = 6 mean.

What i want to know is how you can tell where f''(x) is negative or positive by just looking at the the graph of f(x)

 

[Pwnage101]

the second derivetavie, ie f''(x) determines CONCAVITY, as it determines teh RATE OF CHANGE OF THE GRADIENT OF THE TANGENT, if f''(x) >0, the curve is concave up at that point, if f''(x)<0, the curve is CONCAVE DOWN at theat point, and if f''(x)=0, it is MOST PORBABLY, and in most cases, a point of inflexion - where a curve changes concavity, for example at x=0 for f(x) = x^3

 

[Pwnage101]

by the way f(6) means 'sub in x=6 into f(x)', noy 'y=6' as some stoopid person previously said, and f'(2)=6 means when u sub in x=2 into f'(x), the value u get is 6, ie. teh gradient of the tangent at x=2 on the graph y=f(x) is 6

 

[noobonastick]

the second derivetavie, ie f''(x) determines CONCAVITY, as it determines teh RATE OF CHANGE OF THE GRADIENT OF THE TANGENT, if f''(x) >0, the curve is concave up at that point, if f''(x)<0, the curve is CONCAVE DOWN at theat point, and if f''(x)=0, it is MOST PORBABLY, and in most cases, a point of inflexion - where a curve changes concavity, for example at x=0 for f(x) = x^3

oohhhh thanks, by the way isnt f''(x) < 0 is concave UP?

 

[lyounamu]

oohhhh thanks, by the way isnt f''(x) < 0 is concave UP?

f''(x) is negative, it's actually concave down but it has the MAXIMUM turning point because it's concave-down.