find F''(pi/3)
f(x)= 4cos(x/2)
i got -cos(pi/6) but i don't think that's the correct answer...
Thanks!
To find the second derivative of a function, you need to apply the differentiation process twice. Let's find the second derivative of the given function, f(x) = 4cos(x/2).
First, we find the first derivative of f(x):
f'(x) = -4sin(x/2)*(1/2) = -2sin(x/2)
Now, to find the second derivative, we apply the differentiation process again:
f''(x) = -2cos(x/2)*(1/2) = -cos(x/2)
To evaluate F''(π/3), you substitute π/3 into the derived function, f''(x):
F''(π/3) = -cos(π/3/2) = -cos(π/6)
Since cos(π/6) = √3/2, the correct answer is -√3/2.
Therefore, the correct answer for F''(π/3) is -√3/2.