By "y = −9x2 − 2x" I assume you meant <span>y = −9x^2 − 2x (the "^" symbol represents exponentiation).
Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.
When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.
The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).</span>
Answer:
$27.83
Step-by step explanation:
Answer: D
<u>Step-by-step explanation:</u>
A. False
f(x): x → -∞, y → -∞
g(x): x → -∞, y → 1
B. False
at x = -1, f(x) = -7
at x = -1, g(x) = 1.5
C. False
refer to A
g(x) → 1 and f(x) → -∞ so g(x) > f(x)
D. TRUE
It is hard to tell from the graph so plug in a value to check.
f(10) = 5(10) - 2
= 50 - 2
= 48
g(10) = 2¹⁰ + 1
= 1024 + 1
= 1025
g(10) > f(10)
