please help ! except for 4

2413 2413 . Find the equation of the tangent line. 1. Use the graph of the function f to decide whether the value of the given quantity f (xx) = 2 x+x3 -4x Q X = 1 f ( x ) = 2x/24 x5 -4x exists. If it does, find it. If not, explain why? Y - y1 =m ( x - x 1 ) a) f (-4 ) 5 + b) lim f (x) c) f ( - 2) 6. Use the rules of differentiation to find the derivative of the function. d) lim f (x) a ) s ( t ) = +3 + 5+ 2 - 3t + 8 b) 9 ( x ) = x3 cosx product rule e) f(1) f) lim f (x) c ) g ( t ) = ta Quotient Pure d) f(x ) =314 - 9280 chain rule $' (x) = 1214 - 983(-91 the ax by implicit differentiation. 'dx =1-3x23 x 3 34 2 dy -1 94= a ) x3 y3 - y = x ax (x3342 - 1)=(1- 5x243 product suse dy x 53 2-1 *3342 -1 2 . Evaluate the limits analytically . disI a) lim (-x2+1) factor 8 . Locate the absolute extrema of the function on the closed interval. a. f ( x ) = x3 - 3x2, [ -1,2] a) s'( x) = 3x2-3x/} (-1)=-2.Semin by lim *24x-6 x2 -9 b. f ( x ) =* x243. [-1,1] 0 = 3 X 2 - 3x 3 ( 2) = 2 6 Max 6=3x (x -11 ) (0 ) = 0 3. Find the x-values at which f is not continuous. Which of the discontinuities are 9. f (x) = -x3+ 6x2 -9x -1 3 * =0 x - 1 = 0 f ( 1) =-.05 * = 0 removable? Find the vertical asymptotes and holes. X = 1 a) f(x ) = 7241 a. Find the critical numbers of the function b) f ( x ) = 4-x2 b. Find the open intervals on which the function is increasing or decreasing C. Find the relative extrema x+2 c) f(x) =x2-3x-10 d. Find the intervals where the function is concave up/ concave down e. Find the points of inflection Find the derivative by the limit process . Im (x+Ax)-1(x) Ax 10. 2. Air is being pumped into a spherical balloon at the rate of 7 cubic centimeters per second. What is the rate of change of the radius at the instant the volume equals 367? The volume of a sphere of radius r f ( x ) = = SKIP ! isr. 4 71 -r 3 3 6 71 = 471 4 3 du d+ 7 = 47 1 32 dr d+