16A Practice Midterm II 1.Find the derivative of the following functions. DO NOT simplify your answers. a) f(x)=12x4!7x3+b) g(x)=3tanx2x!9+x1/5secxc) h(x)=(3x3+2x)7+9x2.Find equations of the lines that are tangent to the graph of the function f(x)=x3!6x+5and parallel to the line 3x + y + 4 = 0. Write your answers in slope-intercept form. 3.Use implicit differentiation to find dydxfor the curve xy=y2+x3!1.4.Find all points on the graph of f(x) = cosx – sinx at which the tangent line is horizontal for 0 ≤x < 2π. 5.Use the limit definition of the derivative to prove that ddx[cf(x)]=cddx[f(x)]6.The height (in feet) of a toy rocket above the ground after t seconds is given by s(t)=!16t2+96t+288.a)What are the initial height and initial velocity of the rocket? b)Find the maximum height of the rocket. c)If the rocket hits the ground after 9 seconds, find intervals at which the speed is increasing.
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This note was uploaded on 06/23/2010 for the course MATH math16 taught by Professor Na during the Spring '10 term at UC Riverside.