MATH 1634 Spring 2016 Review Sheet for Exam Two (1) Exam Two is on Thursday, Mar

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MATH 1634 Spring 2016 Review Sheet for Exam Two (1) Exam Two is on Thursday, March 10,2016, covers sections 3.4,3.5, 3.7-3.11, 4.1, and is (2) Do not assume that these are the only problems that will appear on (3) Exam 100 points exercises and quiz questions make good potential test questions will be allowed to test 2. All homework Two will have two parts. You will not be allowed to uase a calculator on Part I. You use one graphing calculator on Part II. Don't forget your calculator you will not be allowed to borrow one during the exam. in boldface below are problems on which you would be allowed to use a graphing calculator The following exercises are extra practice problems for the test: 1. Find the derivative of the following functions. You must simplity your answers. @v"7y=4rs _ 2yF +cosz 2. Find the derivative of the following functions. You do not have to simplify your answers. (z) = He' g(r) = logs r tan (47) gy arctan (z2) - arccos (72) @rt) = (ga Find the slope of the tangent line tod-:-5at (1-1). t(t-1) .3. Find the slope of the tangent line to zs_v=5at (1,-). A spherical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm3/min. At what rate is the diameter changing when the diameter is 10 cm? 5. A kite rises vertically at a rate of 2 ft/s from a point on the ground 5 ft from an observer. Find the rate of change of the angle of elevation of the kite from the observer when the kite is 3 ft above the ground. ve. Given sec y + ry'-z-y, use implicit differentiation to find Given f(x) = 2rs-Zr + 4 and a = 5, find (f-y(a). -S If s t = tt is a given position function, find the ve ity and acceleration functions. Simplify your answers. ( Locate the absolute extrema off(z) = 5a2-10-3 on [0.3]. 10. Find the critical numbers of the following functions. dxla")-x-3ea_24zae following 6-102-3

Explanation / Answer

1a. The given function is y=4/(9*(x^3/21))-2/(3*x^2)-1/(6x)

differentiate with respect to x

dy/dx=d/dx[4/(9*(x^1/7))-2/(3*x^2)-1/(6x)]

the derivative of the function is =dy/dx=-4/(63*x^8/7)+4/(3x^3)+1/(6x^2)

10a. The given function is f(x)=7x^3-39x^2-24x+11

differentiate with respect to x

f'(x)=21x^2-78x-24

Now, our derivative is a polynomial and so will exist everywhere. Therefore the only critical numbers will be those values of x which make the derivative zero. So, we must solve.

     21x^2-78x-24=0

x=[-(-78 )+ or - sqrt{(-78)^2-(4*21*-24)}]/(2*21) (since root of the polynomial foumula [-b+/-sqrt(b^2-4*ac))]/(2a)

x=[78 + or - sqrt{6084+2016}]/42

  x=[78 + or - 90]/42

x=[78 + 90]/42,  x=[78 - 90]/42

so the critical numbers are    x=4,-2/7

  

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