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:
Yes
Step-by-step explanation:
40000 x .10 is 4000 in tax. Total after tax would be 36,000
45,000 × .15 is 6750. Total after tax would be 38,250 which is more
Total hours worked = 5 x 3 = 15 hours
Amount collected = 50 x 15 = $750
Amount paid to the paralegal = 30 x 15 = $450
Amount made by the firm = 750 - 450 = $300
