AP Calc

Test Preparation
1

<p>A function that is continuous is not necessarily differentiable, correct? For example, the derivative of a function from opposite ends might be approach two different points, making that x-value non-differentiable but still continuous if there is a hole in one piece and a point in the other?</p>

<p>A function that is differentiable MUST be continuous.</p>

<p>Correct me if I'm wrong!</p>

<p>P.S.- An even function has y-axis symmetry?</p>

<p>Thanks!</p>

2

<p>A function that is differentiable at a point must be continuous at that point. A function that is differentiable everywhere is continuous. A function that is continuous is not necessarily differentiable.</p>

3

<p>Yeah, you're right. there are different kinds of non-differentiable, continuous functions such as the point on a v-shaped function, called a corner, and the vertical tangent on graphs such as x^(1/3).</p>

4

<p>Right. A point that is differentiable exists and has a slope there, so it must be continuous. However, it is not necessarily differentiable where it is continuous because there can be a corner, a cusp or a vertical/horizontal tangent.</p>

5

<p>An even function has y- axis symmetry. Correct.</p>

6

<p>yupppppppppppp</p>

7

<p>It's sad that I forgot this stuff lol..</p>

8

<p>Differentiability implies continuity by definition.</p>

<p>The graph of the absolute value of x is continuous, but it is not differentiable at all points. There is a cusp at the origin.</p>

9

<p>What is a cusp?</p>

10

<p>a place where the function is continuous but not differentiable, such as f(0) in the function f(x)= absval(x)</p>

11

<p>Is 'cusp' an acronym? Just curious.</p>

<p>Also, how many 3D questions are there on the SAT II Math 2? Can you check out my other thread about math equations if you can help me out in anyway. I'm taking it tomorrow lol..</p>