Thread: Graphs and their Derivatives

essentially, I am given different graphs, and the functions are not given. From the graph, i have to answer where the first derivative is positive or negative, where the second derivative is positive or negative, etc.

I understand when the first derivative is positive and negative (when the gradient of the slope f(x) is positive or negative respectively). I dont understand when the second derivative is positive or negative, its confusing me. Can someone explain...? Thanks for your help.

Think about concavity and points of inflection

Yep, for the second derivative, just look at where is changing in concavity.

so where f'(x) is negative is where f''(x) is positive?

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... =[.

please help im panicking...... just tell me how do i know where the second derivative is negative or positive by looking at the graph.

For intervals when the function f(x) is concave down and for intervals when the function f(x) is concave up.

thanks i guess... but i already got help from somewhere else