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Unformatted text preview: Math 16A Short Calculus, section 2 Practice Final Exam 1. Continuity For each of the following functions, state: the range, the inter val(s) on which the function is continuous, and for each disconti nuity whether or not the discontinuity is removable. (a) y = x 2 + 4 (b) y = x +2 x 2 4 (c) y = 2 b x c (d) y = 4 cos( ) + 1 2. Slope and Derivative (a) Find an equation of the line tangent to f ( x ) = x 2 + 1 with slope 2. (b) Use the limit definition to find the derivative of the following functions. i. f ( x ) = x 2 1 ii. h ( t ) = 2 t 3. Rates of Change (a) The profit P from selling x units of a product is given by P = 15 + 12 x 81 x . i. Find the average rate of change of P on the interval [1 , 9]. ii. Find a formula for the marginal profit. What is the marginal profit for x = 9? (b) A sphere of radius 3 has its radius changing at a rate of 4 inches per second. How quickly is the volume of the sphere changing? 4. Derivative Tests (a) Apply the SecondDerivative Test to find the relative extrema...
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This note was uploaded on 05/22/2011 for the course MATH 16A taught by Professor Sabalka during the Fall '08 term at UC Davis.
 Fall '08
 Sabalka
 Continuity

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