5. If f (x)=(2x+1)^4 then the 4th derivative of f(x)=0 at x = 0 is..

I think you lost the 2's along the way

f'=4( )^3 * 2
f"=24 ( )^2 * 2
f"'=96 ( )*2
f""=192*2 = 384 (= 24*2^4)

Well, if we have the 4th derivative of f(x) equal to 0 at x = 0, it means that the function is as happy as a penguin with a fishy feast! Why? Because it means that at x = 0, the function is as flat as a pancake. So in this case, the 4th derivative of f(x) is simply 0. You can say it's as empty as a library during a clown convention!

To find the 4th derivative of f(x), we need to differentiate the function four times. Let's start by finding the first derivative of f(x):

f'(x) = 4(2x + 1)^3

Next, we can find the second derivative:

f''(x) = 12(2x + 1)^2

Now, let's find the third derivative:

f'''(x) = 24(2x + 1)

Finally, we can find the fourth derivative:

f''''(x) = 24

To find when the fourth derivative of f(x) equals zero, we can substitute x = 0 into the fourth derivative:

f''''(0) = 24

Therefore, the fourth derivative of f(x) is equal to 24 at x = 0.

To find the 4th derivative of f(x) and evaluate it at x = 0, we need to take the derivative of f(x) four times.

First, let's find the first derivative of f(x):

f'(x) = 4(2x+1)^3

Next, we can find the second derivative by differentiating f'(x):

f''(x) = 12(2x+1)^2

Then, to find the third derivative, we differentiate f''(x):

f'''(x) = 24(2x+1)

Finally, we differentiate f'''(x) to get the fourth derivative:

f''''(x) = 24

Now, we can evaluate the fourth derivative at x = 0:

f''''(0) = 24

Therefore, the 4th derivative of f(x) is 24, and it equals 0 at x = 0.

f'=4( )^3 * 2

f"=12 ( )^2 * 2
f'''=24 ( )*2
f""=24*4

So I don't know what your question is, but fourth derivative is not zero.