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.