Hello Tutor Urgent Help Needed with the Calculus Question in the Pictures Below. Solution needed, Thank You!

Use the graph of f to sketch a graph of f'. Choose the correct graph of f'. O A. 8- O B. Ay 6- 107 10 My 8 t 2- 1991 1996 1991 1996 -101 1991 1992 1993 1994 1995 1996 -101 OC. Ay OD. 10- 10My 1991 1996 8 -10- 1996 -10Let f(x) = 2x3 - 6x2 - 48x + 7. a. Find all points on the graph of f(x) at which the tangent line is horizontal. b. Find all points on the graph of f(x) at which the tangent line has slope 96. a. The tangent line is horizontal at the point(s) (Type an ordered pair. Use a comma to separate answers as needed.) b. The slope of the tangent line is 96 at the point(s) (Type an ordered pair. Use a comma to separate answers as needed.)f(a + h) - f(a) a. Use the definition m= lim h to find the slope of the line tangent to the graph of fat P. h-0 b. Determine an equation of the tangent line at P. f(x) =3 + 3x-; P(0,3) a. mian = (Type an integer or a fraction.) b. The equation of the tangent line at P is (Type an equation.)\fAn object thrown vertically upward from the surface of a celestial body at a velocity of 16 m/s reaches a height of s = - 0.812 + 16t meters in t seconds. a. Determine the velocity v of the object after t seconds. b. When does the object reach its highest point? c. What is the height of the object at the highest point? d. When does the object strike the ground? e. With what velocity does the object strike the ground? f. On what intervals is the speed increasing? a. The object's velocity after t seconds is v(t) = b. It takes the object to reach its highest point. (Simplify your answer.) C. The object reaches a maximum height of (Simplify your answer.) d. The object strikes the ground after (Simplify your answer.) e. The object strikes the ground with the velocity (Simplify your answer.) f. The speed is increasing on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)