let f(x)= 2x^2 -8x -3

determine whether function has min or max value and explain why
find min or max value and where it occurs
identify domain and range (ez)

50 fg for that one

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guy has 15 yards of fencing to make rectangular kennel for dog. he will build kennel next to garage, so only needs to enclose 3 sides.

what dimensions maximized area of kennel?

what is the max area?

20 fg for this one

This post was edited by KingStannis on Apr 13 2016 05:47pm

Min or max values occur when the derivative (slope) is equal to zero (horizontal line tangent to original graph).

Did you miss a squared in that? because f(x) = 2x-8x-3 isn't simplified.

yes my bad ty

Kennel area = x *(15-2x) = 15x - 2x^2

Derivative = 15 - 4x

Set derivative = 0 to find min/max

15 - 4x = 0
x = (15/4)

Dimensions = (15/4) by (15 - 30/4)

This post was edited by RzChaos on Apr 13 2016 05:50pm

f(x) = 2x^2-8x-3 --> find derivative with power rule
f'(x) = 4x - 8
Set the derivative equal to zero to solve for the mins/maxes

f'(x) = 4x - 8 = 0
+8 +8
4x = 8
x = 2

f'(x) = 0 when x = 2 (there is a minimum or maximum at x = 2)

f(2) = 2(2)^2 - 8(2) - 3
f(2) = 2(4) - 16 - 3
f(2) = 8 - 19
f(2) = -11

We can further figure out if this is a minimum or a maximum by testing points adjacent to the minimum/maximum.

f(1) = 2(1)^2 - 8(1) - 3
f(1) = 2 - 11
f(1) = -9

since the f(1) is greater than f(2), then there is a minimum at x = 2

Since all powers present in f(x) are positive, there are no discontinuities.
The domain (x) is the element of all real numbers (-infinity,infinity)

Since we know that x = 2 is a minimum, and the minimum value is -11, that is the lowest value of y (inclusive)
The range of f(x) is [-2,infinity)

sending to both of you hope these are right