Evaluate the function f x 2x2 2x 3 at f2 h f2 h f2h Fi

Evaluate the function f (x) = 2x^2 - 2x + 3 at f(2 + h) f(2 + h) - f(2)/h Find the domain of the following f(x) = 3/x - 5 f(x) = 18x/squareroot 3x - 2 Express f(x) = -2x^2 + 20x + 12 in standard form; find its vertex, state if max or min. Find its x- and y- intercept(s). Sketch and show the points you found. When a certain drug is taken orally, the concentration of the drug in the patient\'s bloodstream after t minutes is given by: c(t) = 0.03t - 0.0001t^2 where the concentration is measured in mg/L. When is the maximum serum concentration reached? What is the maximum concentration? Minimize the number mentioned in the following sentence: \"The product of six less than five times a number and one third that same number\"

Solution

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

a) f(2+h) plug x = 2+h

f(2+h) = - 2(2+h)^2 - 2(2+h) + 3

= -2 ( 4+h^2 - 4h ) -4-2h + 3= -8-2h^2+8h-2h-1

adding like terms

f(2+h) = -2h^2 +6h - 9

b) { f(2+h) - f(2) } / h

finding f(2) = -2(2)^2 -2(2) + 3 = -8 -4+3 = -9

plugging the values in { f(2+h) - f(2) } / h

{ -2h^2 +6h - 9 + 9 } / h = -2h + 6

{ f(2+h) - f(2) } / h = -2h + 6

9) f(x) = 3/ (x-5)

domain is all values of x where a function exists

in rational function we cannot divide by zero

setting denominator equal to 0

x - 5 = 0

x = 5

hence , domain is all values of x except x = 5

interval notation

(-infinity , 5 ) U ( 5 , + infinity )

b) f(x) = 18x / sqrt (3x-2)

sqrt (3x-2) > 0

3x -2 > 0

x > 2/3

domain is all values of x greater than 2/3