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The rate of change of the altitude of a hot air balloon rising from the ground is given by y(t) = t3 3t2 + 3t for 0sts10. When is the average rate of change in altitude of the balloon over the time interval 0:510. Kg :- 35 [B . 94 'C. 73 Find the equation of the tangent line to the graph of the given function at the given value of x. f(x) = V(x2 + 18x + 86) A -9,9 B ) 0, -9 C ) 0, 9 D -9If g(2) = 3 and g'(2) = -1, what if the value of at A -1 B -3 C 0 D 2Find the equation of the tangent line at the given value ofx 0n the curve. 2X)! ya = 1. x =1 gift/- x = 1 (5:;- y = -x + 1 Q y = x - 1 A curve has a slope of x+2 at each point (x,y) on the curve. Which of the following is an equation for this curve if it passes through the point (2,1)? 'I:;_\\:," 2x2 + x 8 {ti} x2 2x + 1 {Ca-1x2 x2 + 2x 1 {ti} 1/2 x2 2x 4 Find the equation of the tangent line to the graph of the given function at the given value of x. +28 :35} y = 8/5 x + 64/5 :5: am a}; y = 4/5 x + 64/5 (ti)- 3/ = 3/5 x + 96/5 \fLet f(x) = 1/2 x^6 - 10x# + 12x. What is the value of f(x), when f""(x) = 0 A 5/2 B -3/2 C 1/2 D -23/4Let f(x) = 1/2 x^6 - 10x# + 12x. What is the value of f(x), when f""(x) = 0 A 5/2 B -3/2 C 1/2 D -23/4See the picture below: x=1 A 4 B C 3 Dx2 +3, x#1 If f(x) = then lim = x =1 x-1I (x2 - 2) Vx dx = A 2/5 x- Vx - 4/3 xVx + C B 2/5 x x - 2/3 xVx + C C 2/7 x'vx - 2/3 x x + C D) 2/7 x'vx - 4/3 xVx + CWhat is the instantaneous rate of change at x = -1 of the function f(x) = -V(x2) ? A 2/3 B - 1/3 C - 2/3 D 1/3