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determine whether the function is differentiable (curve has a tangent line) at the indicated point. If it does, find its derivative. if not explain why not.

determine whether the function is differentiable (curve has a tangent line) at the-example-1
User Glenc
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1 Answer

16 votes
16 votes

Let's see the sketch:

The function is differentiable at x = 0 as you can see from the graph. It doesn't have any cusp or discontinuity.

Now, to find the derivate, we use the bottom function (as x = 0 falls in this).

So,


\begin{gathered} f(x)=x^2-x \\ f^(\prime)(x)=2x-1 \\ f^(\prime)(0)=2(0)\text{ -1} \\ f^(\prime)(0)=-1 \end{gathered}

The derivative is -1

determine whether the function is differentiable (curve has a tangent line) at the-example-1
User Eric Zhou
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