Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value. Find that value and explain how you know.Short explanation please.

Answer:x=-1 is a maximum vaue.Step-by-step explanation:To find the minimum and maximum values of the function f(x), we're going to derivate it:f(x) = –5x^2 – 10x + 6 ⇒ f'(x) = -10x - 10The points where f'(x) is zero, could be a maximum or a minimum. Then:f'(x) = -10x - 10 = 0 ⇒ x=-1Now, to know if x=-1 is a maximum or a minimum, we need to evaluate the original function for x when it tends to -1 from the right and from the left. Therefore:For x=-2:f(x) = 6 (Positive)For x=0:f(x) = 6 (Positive)For x=-1f(x) = 11 (Positive)Given that at x=-1, f(x) = 11, and then it goes down to 6 when x=0, we can say that it's a maximum.