Find the value of the derivative of the function f(x)=7-|X| at the extrema point (0,7)?

A. Does not exist
B. 0
C. 7
D. -7

Think about what you know about the shape of |x| functions. They have a cusp, where the slope is discontinuous.

To find the value of the derivative of the function f(x)=7-|x| at the extrema point (0,7), we need to differentiate the function with respect to x and then substitute x=0 into the derivative formula.

The function f(x) can be written as:

f(x) = 7 - |x|

To find the derivative of f(x), we consider two cases: x>0 and x<0.

For x>0, the derivative of f(x) is given by:

f'(x) = 0 - 1 = -1

For x<0, the derivative of f(x) is given by:

f'(x) = 0 + 1 = 1

At x=0, the function is not differentiable, meaning the derivative does not exist. This is because the function has a sharp corner at x=0 due to the absolute value function.

Therefore, the value of the derivative at the extrema point (0,7) does not exist. So, the correct answer is:

A. Does not exist.