What are the excluded values of x for x+4/-3x2+12x+36

x = - 2, x = 6

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make the expression undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

Solve

- 3x² + 12x + 36 = 0 ( divide through by - 3 )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

x = - 2 and x = 6 ← are the excluded values

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50