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

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. :) -
**Reiny**, Friday, December 20, 2013 at 1:37am
8.

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

## Answer this Question

## Related Questions

- Calculus Help - If f(x) = sin(7 − 5x), find f′(π), which is the...
- Precalculus - Use one of the identities cos(t + 2πk) = cos t or sin(t + 2&#...
- Trigonometry - IM STUCK ON THESE :( 1. What is the equation for shifting the ...
- Trigonometry - IM STUCK ON THESE :( 1. What is the equation for shifting the ...
- Math - If y = sin−1 x, then sin y = x,−π/2 ≤ y ≤ &#...
- Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...
- Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...
- biology - Given the part of the molecule shown below, can the underlined atom ...
- Math - Evaluate *Note - We have to find the exact value of these. That I know to...
- caculus - Given f″(x)=−4sin(2x) and f′(0)=3 and f(0)=−6...