Except for c), the others should be simple.View attachment 11721So for number 18 on here I'm not sure how to even figure out if they're true or not
(a) You haven't described your counterexample very well, but you may be thinking about the right thing. Can you give a specific example of f?Okay so for a) False because a symmetric graph across the y axis will have 2 points equal to each other
b) false because f(x) and g(x) is not equal to (f*g)(x)
c) I looked over the mean value, but I'm still not understanding how to implement it
d) I got true because critical points occur at the first derivative equal to zero and critical points are where local extrema is
e) I ended getting false from applying the chain rule
I'm also not very good at calculus so I wouldn't be surprised if I'm still doing these wrong
For (a) you do not need symmetry. Must a function as described in part (a) have an absolute maximum point? Can it have more than one? In my opinion instead of thinking about this you should just draw a continuous function from a to b (do not lift your pen) and see if it has an absolute maximum value. If it has more than one absolute maximum then you should know the answer to the question. If your graph has only one absolute max than ask yourself if you can modify it so it has two or more absolute extremes.Okay so for a) False because a symmetric graph across the y axis will have 2 points equal to each other
b) false because f(x) and g(x) is not equal to (f*g)(x)
c) I looked over the mean value, but I'm still not understanding how to implement it
d) I got true because critical points occur at the first derivative equal to zero and critical points are where local extrema is
e) I ended getting false from applying the chain rule
I'm also not very good at calculus so I wouldn't be surprised if I'm still doing these wrong
c) Suppose that \(\displaystyle a<b\) having the property that \(\displaystyle f(a)=f(b)\).View attachment 11721So for number 18 on here I'm not sure how to even figure out if they're true or not