Chapter 2: Q. 48 (page 222)
Describe the derivatives of each of the piecewise-defined functions in Exercises 45–48.
Short Answer
The derivative of function is
Chapter 2: Q. 48 (page 222)
Describe the derivatives of each of the piecewise-defined functions in Exercises 45–48.
The derivative of function is
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Get started for freeUse the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
After seconds, with
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
The following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
25.
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