Answer:
<em>D. 5 for x less than or equal to 4, equals 2x for x between 4 and 6 including 6, and equals 4 for x greater than 6 Domain: All real number</em>s.
Step-by-step explanation:
Find the complete diagram attached
First we need to get the derivative of the functions
For the function f(x) = 5x - 6
Using the formula
If f(x) = axⁿ
f'(x) = naxⁿ⁻¹
For the function f(x) = 5x - 6
f'(x) = 1(5)x¹⁻¹
f'(x) = 5x⁰
f'(x) = 5
For the function f(x) =x²-2
f'(x) = 2x²⁻¹
f'(x) = 2x
For the function f(x) = 4x+10
f'(x) = 1(4)x¹⁻¹
f'(x) = 4x⁰
f'(x) = 4
Get the domain
The domain is the value of the input variable x for which the functions exists. For the functions given, the domain will be on all real numbers i.e the functions will exists for any value of x on the number line.
Hence Option D is correct
