Explanation Given: The function f ( x ) = 4 x 5 is a probability density function for x ≥ 1 . Formula used: Median : “If X is a random variable with probability function f on [ a , b ] , then the median of X is the number m such that ∫ a m f ( x ) d x = 1 2 ”. Calculation: Consider the given function f ( x ) = 4 x 5 for x ≥ 1 . Use the above mentioned formula and find median. ∫ 1 m 4 x 5 d x = 1 2 (

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Chapter 11.2, Problem 3YT

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To compute: The median for the function f(x)=4x5 .

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

Chapter 11 Solutions

CALCULUS WITH APPLICATIONS

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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The median for the function f ( x ) = 4 x 5 .

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