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Last two CALC questions. :)

posted by on .

8. If f(x) = sin(7 − 5x), find f′(π), which is the derivative at π:

−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. :) - ,

    8.
    f'(x) = -5cos(7-5x)
    f'(π) = -5cos(7-5π)
    = 3.769
    or your last choice of 3.770

  • Last two CALC questions. :) - ,

    #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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