Determine whether f(x)= -5x^2-10x+6 has a maximum or minimum value and find that value:?

Question

a. minimum, -1
b. maximum, 11
c. maximum, -1
d. minimum, 11

Answer 1

To determine whether f(x) = -5x^2 - 10x + 6 has a max or min value, we have to complete the square.

f(x) = -5x^2 - 10x + 6

First thing you do is factor -5 out of the first two terms.

f(x) = -5(x^2 + 2x) + 6

Now, complete the square within the brackets by adding +1. Note that we have to offset this by adding +5 outside the brackets.

f(x) = -5(x^2 + 2x + 1) + 6 + 5

Now, merge the 6 and the 5.

f(x) = -5(x^2 + 2x + 1) + 11

This makes our maximum equal to 11 (the number outside the brackets). We know it is a maximum because the number in front of the brackets is a negative number (-5).

Answer 2

Or you can take the derivative.
f'(x)=-10x-10
Set it equal to zero. 0 = -10x-10
-10x=10
x=-1
Use a sign chart. It changes sign from positive to negative at x=1, so it's a maximum.
Plug in 1 to f(x)
f(1)=11
Maximum point at (1,11)
x being 1, and value 11. Answer is B.

OR

You know it's a downward parabola. Since the coefficient is negative.
You know it's in the form of a frown, so it has to have a maximum, not minimum. Find the axis of symmetry, which is
(-b)/2a= x
-(-10)/2(-5)=x
10/-10= -1 = x
Plug it in for f(x) again. Answer still B.

Answer 3

for y = ax^2 + bx +c then if a is beneficial, the function has a minimum. If a is destructive, the function has a optimum. Differentiate the function. You get 2ax+b. The minimum or optimum is the place the dervative is 0 provided that's the place the slope is 0. that's because of the fact if the slope isn't 0, then shifting to the left or the spectacular alongside the curve could bring about a enhanced or decrease cost, so the standards the place the slope isn't 0 won't be in a position of be maximums or minimums. sparkling up for x while the spinoff 2ax+b is 0. You get x=-b/2a. that's the x place the place the minimum or optimum occurs. Plug x=-b/2a into the unique equation and you get the fee of y on the min or max, that's the minimum or optimum of the function.

Answer 4

Maximum because the coefficient of x^2 is negative.
The maximum occurs when x= 10/-10 = -1
So max = -5+10+6 = 11
The aanswer = b

Answer 5

If it's a strict multiple-choice problem, you can solve it in two easy steps without knowing anything beyond simple arithmetic:

1. Try x=0.
f(x)=6, eliminating answers c and d.

2. Try x=enormous.
f(x) is enormously negative, eliminating answer a (and re-eliminating d).

The only answer left is b.

Time required: a few seconds.
Algebra knowledge required: none.

The problem would be much harder if there were a fifth choice:
"e. None of the above". :-)

Answer 6

It has a maximum since the leading coefficient is negative and its maximum valuse is 11. Therefore, the answer is b.

Answer 7

b. maximum, 11

are u useing us for your homework or testing us to see how dumb we are? lol :P~

~Lady Yuna of the wind