Last two CALC questions. :)
posted by Samantha .
8. If f(x) = sin(7 − 5x), find f′(π), which is the derivative at π:
9. Given the function:
Find the value of b, if any, that will make the function differentiable at x = 0.
No such value exists.
There is not enough information to determine the value.
f'(x) = -5cos(7-5x)
f'(π) = -5cos(7-5π)
or your last choice of 3.770
#9.first, you need
0+b = cos(0)
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: