Step 7 To estimate the slope of the tangent line at t = 15, we average the slopes of the adjacent secant lines for t = 10 and t = 20. As obtained in part (a), those slopes are msec = -136 and msec = -114.4, respectively. Therefore, the slope of the tangent line at t = 15 is as follows. (In the last step, round your answer to one decimal place.) -136 + If you use a graph of the function to estimate the slope of the tangent line at P(15, 1,040), you will see that it matches the above result. Submit Skin (you cannot come back)

2. Evaluate these derivatives

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)

The shadow cast by a man standing 1 m from a lamppost is 1.2 m long. If the man is 1.8 m tall and walks away from the lamppost at a speed of 120 m/min, at what rate is the shadow lengthening after 5 s? Write what is given and what you need to find. Draw the diagram. Show the derivative step. Write the conclusion statement.

Find derivative and explain step by step