Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
f(x) = -(x – 6)2 – 1
The
value is

Step-by-step explanation:

f(x) = -(x-6)² - 1 = -(x² - 2×6x + 6²) - 1 = -x² + 12x - 37

since x² has a much bigger progression than 12x for growing values of x (and the constant -37 plays no role at all), -x² and with it the whole expression goes to -infinity when x goes to + or - infinity.

so, depending on the directions from your teacher the minimum is either -infinity or does not exist (as infinity is not a value).

now the maximum is at the extreme point of the curve. that is at the point where the square function curve turns around.

the easiest way to find this is finding the x value, for which the first derivative of f(x) is 0.

f'(x) = -2x + 12

-2x + 12 = 0

12 = 2x

x = 6

so, the maximum for f(x) happens at the point x=6.

and what is f(6) ?

f(6) = -(6)² + 12×6 - 37 = -36 + 72 - 37 = 72 - 73 = -1

so, the maximum of f(x) = -1

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

the answer is c)8

step-by-step explanaction: