MHB 2.1.4 AP calc exam graph properties

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The discussion revolves around interpreting a graph that represents the derivative of a function rather than the function itself. Participants express confusion about identifying properties of the graph and how it relates to the original function. One user mentions choosing option B based on clarity, while another acknowledges that understanding the derivative graph significantly aids in their comprehension. The conversation highlights the importance of recognizing graph properties in calculus, particularly for AP exam preparation. Overall, mastering derivative graphs is crucial for success in AP Calculus.
karush
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Screenshot 2020-09-21 at 7.13.21 PM.png

screenshot to avoid typos

I picked B just could see the others as definite

insights?
 
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note the graph is the derivative of f, not f ...

(D)

deriv_graph.jpg
 
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I always get ? with these graphs but that helps a lot
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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