The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 the function g is given by g(x)=eax+f(x) for all real numbers, where a is a constant. find g ′(0) and g ″(0) in terms of a. show the work that leads to your answers. the function h is given by h(x)=cos(kx)[f(x)]+sin(x) for all real numbers, where k is a constant. find h ′(x) and write an equation for the line tangent to the graph of h at x=0. for the curve given by 4x2+y2=48+2xy show that dy dx = y−4x y−x . for the curve given by 4x2+y2=48+2xy, find the positive y-coordinate given that the x-coordinate is 2. for the curve given by 4x2+y2=48+2xy, show that there is a point p with x-coordinate 2 at which the line tangent to the curve at p is horizontal.

The minimum wage in washington has been increasing over the last ten years. years 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 washington state minimum wage $6.50 $6.72 $6.90 $7.01 $7.16 $7.35 $7.63 $7.93 $8.07 $8.55 $8.55 a) find the linear regression equation for the minimum wage in washington using this data ( x  0 in 2000). round to the thousandths. b) what is the slope? specifically, what does the slope represent in the real world context? c) what is the y-intercept? specifically, what does the y-intercept represent in the real world context? d) write your equation as a function of x. e) if you do not earn a college degree and you are earning minimum wage in 2020, what do you predict you will be earning per hour with the linear regression equation? f) if the trend continues, when will the minimum wage be $15 an hour? 3. why are your answers to #1d and #2a above different? which do you think is more accurate (#1 or #2) and why

What are the solutions of the system? solve by graphing. y = x^2 + 3x + 2 y = 2x + 2

Sam is a waiter at a local restaurant where he earns wages of $5 per hour sam figures that he also eams about $3 in tips for each person he serves sam works 6 hours on a particular day. if n represents the number of people sam serves that day, which of the following functions could sam use to figure ehis total earings for the do o a. en) = 30 o b. en) = 5n+ 18