Consider the following function and point. =X+2, (3,5) (a) Find an equation of the tangent line to the graph of f at the given point. y = f(x) = (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. (Select the correct graph.) y y 5 10 7- -10 15 10 5 10 -10 +10 -15 ℗

y= 14x-2 6, *=4 Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. 1 y= 14x +2x+6; x=4 + 2x +6; x= 4 The slope of the tangent line to the graph at the point x= 4 is. (Simplify your answer.)

Can you please do all of them. Thank you :)

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)