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Chapter 2: Q. 72 (page 211)
Each of the equations in Exercises 69鈥�80 defines y as an implicit function of x. Use implicit differentiation (without solving for y first) to find
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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鈥�38.
25.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of at the point
In Exercises 69鈥�80, determine whether or not is continuous and/or differentiable at the given value of . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
On earth, A falling object has a downward acceleration of 32 feet per second per second due to gravity. Suppose an object falls from an initial height of ,With an initial velocity of feet per second, Use antiderivatives to show that the equations for the position and velocity of the object after t seconds are respectively and
Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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