Mathematics, 01.07.2019 05:10 kayranicole1

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 .

Answers: 1

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Answer from: lazymarshmallow7

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 from: 21villalobosjabez

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)

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

in simplified version it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

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Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value. find that value and expla...