# Tangent Line - Applied Calculus - Quiz, Exercises for Calculus. Allahabad University

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Some keywords in Applied Calculus are Exponential Model, Derivative, Frozen Pizza, Speeding Driver, Anti-derivative, Tangent. Some points of this exam are: Tangent Line, Fact, Derivative, Equation, Stock Is Falling, Lev...
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Prof. S. Brick Math 120 Spring ’02 Applied Calculus; Quiz 6 – redone section 2

1. Suppose you know for a fact that the derivative of f(x) = x3 is f ′(x) = 3x2. Find the equation of the tangent line at x = 2.

2. Suppose P (t) is the price of a stock as a function of time. What does the statement “The price of the stock is falling but leveling off” say about the sign of P ′(t) and P ′′(t) ?

3. Sketch two copies of the graph of y = x2 from x = 1 to x = 2 and in one draw two evenly-spaced rectangles using left-hand endpoints, in the other two evenly-spaced rectangles using right-hand endpoints. Which one underestimates the area ? Which one overestimates the area ?