Calculus :

61-63:

Find an equation of the tangent line to the curve at the given point. y = r (81. 9) Need Help? _'__ 62. [-12 Points] SESSCALCZ 2.1.018. If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). Need Help? _ Find 1' '(a). 2t+8 t+7 Need Help? f0?) = 69. [-I4 Points] DETAILS SESSCALCZ 2.1 .502.XP. If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height (in meters) after t seconds is given by H = 151' 1.86t2. (a) Find the velocity of the rock after two seconds. m/s (b) Find the velocity of the rock when t = .3. m/s (c) When will the rock hit the surface? (Round your answer to one decimal place.) t = s (d) With what velocity will the rock hit the surface? m/s Need Help? _' Find the derivative of the function using the definition of derivative. 7 em = W State the domain of the function. (Enter your answer using interval notation.) S State the domain of its derivative. (Enter your answer using interval notation.) Z Need Help? _ 74. [3/5 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 2.2.043. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the definition of a derivative to find f'(x) and f"(x). f ( x ) = 3x2 + 4x + 2 f' ( x ) = f" (x) = Graph f, f', and f" on a common screen and check to see if your answers are reasonable. We see from the graph that our answers are reasonable because the graph of f' is that of a linear function and the graph of f" is that of a constant function. Need Help? Read It 75. [4/8 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 2.2.044. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If f(x) = 4x2 - x3, find f'(x), f"(x), f""(x), and f(4)(x). f' ( x ) = f " ( x) = f " (x) = F ( 4 ) ( x ) = Graph f, f', f", and f" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? The graphs are consistent with the geometric interpretations of the derivatives because f' crosses the x-axis @ where f has a slope of m = 0, f" crosses the x-axis @ where f' has a slope of m = 0, and f" is a straight line function equal to the slope of f". Need Help? Read It Watch ItFind the derivative of the function using the definition of derivative. 60) = 6t t+ 9 State the domain of the function. (Enter your answer using interval notation.) S State the domain of its derivative. (Enter your answer using interval notation.) Z Need Help? _'_' 77. [-/6 Points] DETAILS SESSCALC2 2.2.510.XP. Use the given graph to estimate the value of each derivative. y = f(x) 0 (a) f'(0) (b) f'(1) ( c) f' (2 ) (d) f'(3 ) (e) f'(4) (f ) f' (5 ) Need Help? Read It 78. [-/1 Points] DETAILS SESSCALC2 2.3.001. Differentiate the function. f(x) = 270 f'( X ) = Need Help? Read ItDifferentiate the function. 1 ft =6t () 3 Need Help? Differentiate the function. _ 2 10 F _ _ (X) 5X Need Help? _ Differentiate the function. f(x)=x57X+6 Need Help? Differentiate. f(x) = 9x5 7 cosx