What is the equation of the line tangent to the function f (x)= 3 x^2+ x at the point(-2,4 )?

First we'll require the derivative (slope) function.

f'(x) = 6x + 1

Next evaluate the derivative function @ x = -2

f'(-2) = 6(-2) + 1
f'(-2) = -11

Thus the slope of the tangent line @ x = -2  is  m = -11

Now we can use either  y = mx + b  or  y - y1 = m(x - x1)  to find the tangent equation.

y - 4 = -11(x - (-2))
y - 4 = -11(x + 2)
y - 4 = -11x - 22
     y = -11x - 22 + 4

Thus

y = -11x - 18  or  11x + y + 18 = 0  is the equation of the required tangent.

Answer and Step-by-step explanation:

C(x) be the statement "x has a cat"

D(x) be the statement "x has a dog"

F(x) be the statement "x has a ferret".

Universe = x = all students in your class.

a)A student in your class has a cat, a dog and a ferret   = ∃x(C(x) ∧ D(x) ∧ F(x))

b)All students in your class have a cat, a dog, or a ferret  =  ∀x(C(x) ∨ D(x) ∨ F(x))

c)Some students in your class has a cat and a ferret but not a dog  = ∃x (C(x) ∧ F(x) ∧ ¬D(x))

d)No student in this class has a cat, a dog and a ferret  ¬∃x (C(x) ∧ D(x) ∧ F(x))

e)For each of the three animals, cats, dogs and ferrets, there is as student in your class who has one of the three animals.  (∃xC(x)) ∧ (∃xD(x)) ∧ (∃xF(x))