Let h be a twice-differentiable, decreasing function of t. If h(-5) = 40 and h(15) = –20, whichof the following must be true on the interval (-5, 15) ?(A) h(t) is strictly decreasing on the interval.(B) h(t) has a tangent line with a slope of –3 for some t in the interval.(C) h(t) is concave down for all t in the interval.(D) h(t) is concave up for all t in the interval.AВ

Introduction: The mean value theorem asserts, approximately, that for each planar arc between two…

Answered: Let h be a twice-differentiable,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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How would a small change in your average gas mileage (in miles/gallon) change the number of gallons of gas you use per month? More specifically, do the following: (a) Give numerical evidence that supports or refutes the claim that a small change in your average gas mileage results in an approrimately small change in the number of gallons of gas you use each month. Choose the distance you drive each month (and keep this constant) and then at least two significantly different values for the average gas mileage. Approrimate the proportionality constant in each case (if it erists) and write the proportionality approxima- tions. Be sure to define the appropriate variables and pay particular attention to units. (b) Using your results from part (a), approximate the proportionality con- stants that relate the small relative change in the number of gallons of gas
7. The function describing personal consumption for the US economy from 1929 to 1941 was C(X) = .712X +95.05, where C(X) is the personal consumption expenditure and X is the personal income, both measured in billions of dollars. Find the rate of change in consumption with respect to income. Interpret this result.
(x² + 1)(x +3)² 18. Find the derivative of y = In %3| x -1
The graph below is the derivative of the function y = f(x) on the interval x [-3,10. Suppose f(x) is continuous and f(-1) = 1. Determine the value of the original function f(x) at x = -3, x = -2, and x = 1. Enter f(-2) in the blank below.
Suppose the derivative of a function f(x) is df/dx = (x-8)(x+4)(x-3). Are the below values local minima, local maxima, or neither? x = -8 x = -4 x = 3 x = 12
Letf (x) = 3x – 2 – 4x². Find the max/min and using the first derivative test determine if it is a min, a max, or an inflection point. x*=3/8, max Ox*=3/8, min Ox*=8/3, inflection point Ox*=3/8, inflection point ) x*=8/3, max Ox*=8/3, min

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