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July 23, 2014

July 23, 2014

Posted by **Samantha** on Friday, December 20, 2013 at 12:59am.

−0.754

−0.657

0

* 0.657

3.770

9. Given the function:

g(x)={x+b, x<0

{cos(x), x≥0

Find the value of b, if any, that will make the function differentiable at x = 0.

0

1

* 2

No such value exists.

There is not enough information to determine the value.

- Last two CALC questions. :) -
**Reiny**, Friday, December 20, 2013 at 1:37am8.

f'(x) = -5cos(7-5x)

f'(π) = -5cos(7-5π)

= 3.769

or your last choice of 3.770

- Last two CALC questions. :) -
**Steve**, Friday, December 20, 2013 at 5:36am#9.first, you need

0+b = cos(0)

so b=1

Now f is continuous

But you also need the derivative to be defined at x=0, so

1 = -sin(0)

But it does not. What that means is the left limit and right limit do not agree, so g' has a break at x=0.

If you plot both parts of g(x), you can see that the slope changes abruptly at x=0:

http://www.wolframalpha.com/input/?i=plot+y%3Dx%2B1+and+y%3Dcos%28x%29

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