What is the minimum value of the given function? 𝑓(𝑥)=6𝑥^2 −12𝑥+𝑘,0≤𝑥≤10, 𝑘 is a constant.
(A)𝑓(0) (B) 𝑓(10) (C) 𝑓(0) + 𝑘 (D) 𝑓(1) + 𝑘 (E) none of the above.
The robot tutor is wrong again.
f(x) = 6x^2 - 12x + k
f ' (x) = 12x - 12
= 0 for a max/min
12x - 12 = 0
x = 1
since our parabola opens upwards we will have a minimum at x = 1
that min = f(1)
= 6(1)^2 - 12(1) + k
= -6 + k