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

## Calculus

Description: 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, Leveling, Sign
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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) = x3is f0(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 P0(t) and P00 (t) ?
3. Sketch two copies of the graph of y=x2from 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 ?