Find the derivative of y = 22 + 1 7z dy dzFind the derivative of f(x = 2 7 f' (ac)\fIf f(a) = 23 + 4.5x2 - 54x + 2, find analytically all values of x for which f'(x) = 0. (Enter your answer as a comma separated list of numbers, e.g., -1,0,2) C =12 + +3 - 1 Find the derivative of f(t) = +4 f' (t ) =\fFind the derivative of f(t) = et+6 answer =The height ofa sand dune (in centimeters) is represented by f(t) : 500 5752 cm, where t is measured in years since 1995. Find f(8) and f' (8), and determine What each means in terms of the sand dune. Give the values of f (8) and f' (8) below, including Find an equation for the line tangent to the graph of f at (3, 98), where f is given by f(x) = 5x3 - 5x2 + 8. y =Certain pieces of antique furniture increased very rapidly in price in the 19705 and 19803. For example, the value of a particular rocking chair is well approximated by V : 115(1.3)t, Where V is in dollars and t is the number of years since 1975. Find the rate, in dollars per year, at which the price is increasing. rate = dollars/yr Find the derivative of the function y(a:) : km + 33'\". Assume that k: is a positive constant. y'($) : For fx 3 64 find f'(x). f' (2)Let f(x) = 6 sin x + 6 cos x f' (ac) = f' ( - # ) =(1 point) A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 1 sint, where t is in seconds and a in centimeters. (a) Find the velocity at time t. (b) After finding the velocity of the mass at time t = 27/3, in what direction is it moving at that time? Answer "I" for left or "r" for right below. equilibrium position V O X v(t) = direction:\fFind the equations of the tangent line and normal lines to the graph of the function f(x) = 8 sin x at x = 1 /2. a) Tangent line: ? b) Normal line: ? VLet f(x) = 5 sin(x) + 6 cos(x). Find the following: 1. f'(x)= 2. f' (2) =In this problem, please evaluate the trig functions without a calculator and do not use a decimal point in your answer. An equation of the tangent line to the curve y : sin(m) at a: : 77r/ 4 is y: + -(x77r/4). An equation of the tangent line to the curve y : cos(ac) at :c : 277/ 3 is y: + '(ZE27T/3>. For What values of m in [0, 2%] does the graph of x) 2 :5 + 2 51113; have a horizontal tangent? List the values of :1: below. Separate multiple values with commas. m