SOLUTION: A function is given. What is the minimum value of the function? 𝑓(𝑥)=3𝑥^2 −11𝑥+𝐶, 5≤𝑥≤10, 𝐶 is a constant (A)𝑓(5) (B) 𝑓(10) (C) 𝑓(11/3) (D)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A function is given. What is the minimum value of the function? 𝑓(𝑥)=3𝑥^2 −11𝑥+𝐶, 5≤𝑥≤10, 𝐶 is a constant (A)𝑓(5) (B) 𝑓(10) (C) 𝑓(11/3) (D)       Log On


   



Question 1189469: A function is given. What is the minimum value of the function?
𝑓(𝑥)=3𝑥^2 −11𝑥+𝐶, 5≤𝑥≤10, 𝐶 is a constant
(A)𝑓(5) (B) 𝑓(10) (C) 𝑓(11/3) (D) 𝑓(11/6) (E) none of the above.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

x-coordinate of the vertex is  x = " -b%2F%282a%29 " = -+%28-11%29%2F%282%2A3%29 = 11%2F6 = 1.8333...



To the right from this point on x-axis, this quadratic function increases monotonically, 

so its minimum value in the given interval/segment is at x=5, i.e. f(5).    ANSWER


Option (A).

Solved and explained.