Answer:
(a) y = 9/4x -1/4
(b) (-2, -2), (-2, 2)
(c) see below
Step-by-step explanation:
(a) The derivative can be found from ...
2y·y' = 3x² +6x
At (x, y) = (1, 2), this is ...
4y' = 9
y' = 9/4
so the equation of the tangent is ...
y = (9/4)(x -1) +2
y = (9/4)x -1/4
__
(b) At y' = 0, we have ...
0 = 3x² +6x = 3x(x +2)
This says y' = 0 at x=0 or x=-2. (x = 0 is an extraneous solution.)
At x = -2, we have ...
y² = (-2)³ +3(-2)² = -8+12 = 4
y = ±2
So, the horizontal tangent points are (x, y) = (-2, ±2).
Answer:
Step-by-step explanation:
If you plot the focus and the vertex, you see that the focus is on the same vertical line, just 4 units up. Since the vertex is below the focus and a parabola ALWAYS wraps around the focus, the parabola is a positive y equals x-squared type. Depending upon what you call standard form will dictate how your answer "looks", although they are both the same parabola. There are 2 forms:
and
We will work on the first one, then rewrite it into the second one.
Our h value is -5, our k value is 2 (from the vertex (h,k)), and p is defined as the distance between the focus and the vertex. Our p is 4. Filling all that in:
That's one form. If we expand the left side of that form we have
Now divide both sides by 16 to get
Now add 2 to both sides in the form 32/16 to get
They are both the same parabola; pick whichever one fits your needs.
Answer:
Step-by-step explanation:
f(x)=1/(x+1)
f(x)=1/(-0.99+1)=100
i can't see the last choice but i gave an example
i hope it works
Answer:
VOLUME:
amount of confetti stuffed in a tube
amount of soup in a can
amount of dirt in a flower pot
SURFACE AREA:
amount of paper to cover a can
amount of paint for outside of tube
amount of cardboard to make a tube
Step-by-step explanation: