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 - 10
The points where f'(x) is zero, could be a maximum or a minimum. Then:
f'(x) = -10x - 10 = 0 ⇒ x=-1
Now, 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=-1
f(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.
Answer:
max at (-1,11)
Step-by-step explanation:
f(x) = –5x^2 – 10x + 6
This parabola opens downward
f(x) = ax^2 + bx+c
The value a is negative, so it opens down.
Because it opens down, it will have a maximum
We can find the x value of the maximum by finding the axis of symmetry
h = -b/2a
h = -(-10)/2(-5)
= 10/-10
h= -1
The x value of the vertex is -1
To find the y value, substitute this back into the equation
f(-1) = -5( -1)^2 - 10(-1) +6
=-5(1) +10+6
=-5 +10+6
=11
The maximum is at (-1,11)
