A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and at an angle of 45◦ with respect to the ground. The path of the baseball is given by the function ?(?)=−0.0032?2 + ? + 3 where f(x) is the height of the baseball feet) and is the horizontal distance from home plate (in feet).? a) Determine the axis of symmetry of f(x), and sketch the graph of ?(?) for . (2)0≤?≤300? B) What is the maximum height reached by baseball and how far from the home plate does that occur ? (1) C) Find f(0) and interpret the result in the context of the problem. (1)?

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

solve and graph the second derivative test of this function

Given the function y = 1+4vx- 2 i) Find the domain. ii) With the aid of a table of values, sketch the graph. State the range of f(x). iii) Determine the slope of the tangent line to the curve at the point (11,13).

Find ?(?) if ?(0) = 4 and the slope of the tangent line is 4?3 + 2?.

Find an equation of the tangent line to the curve at the given point. x2 (3,9) y (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equation in terms of y and x.) equation of the tangent line: