A continuous function but not diffrentiable at a point

Test Preparation AP Test Preparation
1

<p>2008, form B ,question 5 AP</a> Central - The AP Calculus AB Exam</p>

<pre><code> They put the graph of g', and it is a bunch of continuous straight lines, now where exactly is the function non diffrentiable? when it has a horizontal tangent? or a vertical tangent? and what is the slope at both if there is any?
</code></pre>

2

<p>g’ is not differentiable where the left hand limit of the derivative of g’ does not equal the right hand limit of the derivative of g’. Therefore, MVT does not apply because the line segments of g’ have sharp terms (i.e. g’’ is not continuous, and therefore g’ is not differentiable).</p>

3

<p>Graphs are only differentiable where the graph is continuous and has a smooth curve. There are sharps corners (called cusps) on the graph which means the graph is not differentiable at those points.</p>