Your last submission is used for your score. 1. [-/1 Points] DETAILS LARCALCET7 3.2.031. MY NOTES ASK YOUR TEACHER Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function Point f ( x ) = 27 (3, 3) f ' ( 3 ) = 2. [-/2 Points] DETAILS LARCALCET7 3.2.059. MY NOTES ASK YOUR TEACHER Consider the given function and point. f(x) = -7x4+ 10x2 - 3, (1, 0) (a) Find an equation of the tangent line to the graph of the function at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results. y w 2 2 X X * X - 3 -2 2 3 -3 -2 2 3 -3 -2 2 3 -3 -2 2 3 -1 -1 -2 N -3 O O O O3. [-/2 Points] DETAILS LARCALCET7 3.3.019. MY NOTES ASK YOUR TEACHER Find f'(x) and f'(c). Function Value of c f( x ) =x - 9 x - 8 = 1 f' ( x ) = f' ( c ) = 4. [-/1 Points] DETAILS LARCALCET7 3.4.017. MY NOTES ASK YOUR TEACHER Find the derivative of the function. h (s ) = -2\\ 752 + 1 h' ( s ) = 5. [-/1 Points] DETAILS LARCALCET7 3.4.078. MY NOTES ASK YOUR TEACHER Find the derivative of the logarithmic function. y = In( V x2 - 9) y'= 6. [-/1 Points] DETAILS LARCALCET7 3.5.050. MY NOTES ASK YOUR TEACHER Use implicit differentiation to find an equation of the tangent line to the graph at the given point. x2 + xy + y2 = 16, (4, 0) y ( x ) =7. [-/1 Points] DETAILS LARCALCET7 3.6.018. MY NOTES ASK YOUR TEACHER Find the derivative of the function. f(t) = arccsc(-t2) f' (t ) = 8. [-/1 Points] DETAILS LARCALCET7 3.6.026. MY NOTES ASK YOUR TEACHER Find the derivative of the function. h(x) = x2 arctan(9x) h' ( x ) = 9. [-/2 Points] DETAILS LARCALCET7 3.7.508.XP. MY NOTES ASK YOUR TEACHER Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = 2 (x2 - 3.x) (a) Find dy/dt when x = 5, given that dx/dt = 2. dy/dt = (b) Find dx/dt when x = 6, given that dy/dt = 1. dx/dt = 10. [-/1 Points] DETAILS LARCALCET7 3.7.026. MY NOTES ASK YOUR TEACHER An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 250 miles per hour. What is the speed of the airplane? mph 6 mi Not drawn to scale