121616949-math.53

# 121616949-math.53 - 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-1 8 6 4...

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2.4 The Derivative Function 39 0 1 - 2 - 1 0 1 2 ................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................ Figure 2.2 A cusp on x 2 / 3 . Exercises 1. Find the derivative of y = f ( x ) = 169 - x 2 . 2. Find the derivative of y = f ( t ) = 80 - 4 . 9 t 2 . 3. Find the derivative of y = f ( x ) = x 2 - (1 /x ). 4. Find the derivative of y = f ( x ) = ax 2 + bx + c (where a , b , and c are constants). 5. Find the derivative of y = f ( x ) = x 3 . 6. Shown is the graph of a function f ( x ). Sketch the graph of f ± ( x ) by estimating the derivative at a number of points in the interval: estimate the derivative at regular intervals from one end of the interval to the other, and also at “special” points, as when the derivative is zero. Make sure you indicate any places where the derivative does not exist.
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Unformatted text preview: 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-1 .-. 8-. 6-. 4-. 2 0.0 0.2 0.4 0.6 0.8 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................................................... . . .. ................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Shown is the graph of a function f ( x ). Sketch the graph of f ± ( x ) by estimating the derivative at a number of points in the interval: estimate the derivative at regular intervals from one end of the interval to the other, and also at “special” points, as when the derivative is zero....
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