Ron charges $10 to park a car in his parking lot. He pays $50 per day to rent the lot. If 40 cars park in his lot during the day
2 answers:
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a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
Evaluate the integral to solve for y :
Use the other known value, f(2) = 18, to solve for k :
Then the curve C has equation
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
The slope of the given tangent line is 1. Solve for a :
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
So, the point of contact between the tangent line and C is (-1, -3).
Well, for a line with a slope of 3/4, any other parallel line to it, will also have the same slope of 3/4
so if the line through (2, -1) is parallel to it, it has a slope of 3/4 as well
so if the line through (2, -1) is parallel to it, it has a slope of 3/4 as well