The function f(x) = 4x² – 16x + 6 has a minimum value is –10 when the value of x is 2. Then the correct option is B.
What is differentiation?
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given below.
[tex]f(x) = 4x^2 -16x + 6[/tex]
Differentiate the function, then we have
[tex]\dfrac{d }{dx} f(x) =\dfrac{d}{dx}(4x^2 -16x + 6) \\\\ \dfrac{d }{dx} f(x) =8x - 16 \\[/tex]
The value of x will be
[tex]8x - 16 = 0\\x = 2[/tex]
Then again differentiate the function, if the value comes negative then maxima and if the value is positive then minima.
[tex]f''(x) = \dfrac{d }{dx} f'(x) \\\\f''(x)=8x - 16 \\\\f''(x) = 8\\\\ f''(x) > 0[/tex]
Then the function is minimum at 2.
More about the differentiation link is given below.
https://brainly.com/question/24062595
