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

−0.754
−0.657
0
0.657
3.770

I chose 0.657 ... I did not really get this exact answer, its just that while I was trying to figure this out my answer was actually 0.6978 but I just kind of assumed it was D...So did I get this right?

It is not a matter of "choosing" here, you must calculate it.

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

f '(π)
= -5cos(7-5π)
= 5cos(-8.7078..) = 3.770

Did you set your calculator to radians in your DRG mode ?

Ha.. I was just using a old fashion calculator and hoping I could do the rest in my head. But thanks I think I understand now. =D

Well, it's great that you made an effort to solve the problem! However, I have to be the bearer of bad news - your answer of 0.6978 is not quite correct. But hey, close enough, right? Close only counts in horseshoes and hand grenades, my friend.

The actual correct answer is -0.754. So unless you're having an upside-down day, it looks like your assumption was a bit off this time. But don't worry, I'm sure you'll nail it next time! Keep up the good work!

To find the derivative of f(x) = sin(7 - 5x), we can apply the chain rule. The chain rule states that if we have a composition of functions, such as sin(g(x)), then the derivative is given by the product of the derivative of the outer function (sin) with respect to the inner function (g(x)), multiplied by the derivative of the inner function (g'(x)).

In this case, the outer function is sin and the inner function is 7 - 5x.

1. Let's first find the derivative of the inner function (g'(x)):
g'(x) = d/dx (7 - 5x)
= -5

2. Now, let's find the derivative of the outer function (sin) with respect to the inner function (7 - 5x):
d/dx (sin(7 - 5x)) = cos(7 - 5x)

3. Finally, we can multiply the derivative of the outer function with respect to the inner function by the derivative of the inner function:
f'(x) = g'(x) * d/dx (sin(7 - 5x))
= -5 * cos(7 - 5x)

To find f'(π), we substitute x = π into the derivative:
f'(π) = -5 * cos(7 - 5π)

Now, we can use a calculator to evaluate this expression:
f'(π) ≈ 0.657

So, the correct answer is option D: 0.657. Therefore, you did get it right!

To find the derivative of the function f(x) = sin(7 − 5x), you need to use the chain rule. Let's break down the steps to find f'(π):

1. Take the derivative of the outer function:
The derivative of sin(x) is cos(x).

2. Take the derivative of the inner function:
The derivative of 7 − 5x with respect to x is -5.

3. Apply the chain rule:
Multiply the derivative of the outer function (cos(π)) by the derivative of the inner function (-5).

Now let's calculate f'(π):

f'(x) = cos(7 − 5x) * (-5)

Substituting x = π:

f'(π) = cos(7 − 5π) * (-5)

Using a calculator to evaluate cos(7 − 5π) ≈ 0.657, we have:

f'(π) ≈ 0.657 * (-5)
f'(π) ≈ -3.285

Therefore, the correct answer is approximately -3.285, not 0.657.

It seems like you made an error in your calculation or used an incorrect value for cos(7 − 5π). You should double-check your calculations to find the correct derivative.