For the given function, (a) find the slope of the tangent line to the graph at the given point; (b) find the equation of the tangent line. g(x)=5√√x at x=16 (a) The slope of the tangent line at x = 16 is ☐ -
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- a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. y = (3x +7) x? a) Use the Product Rule to find the derivative of the function, Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is (3 x +7)x² + B. The derivative is ( )x + ( x. C. The derivative is (3 x +7) (D O D. The derivative is (3Vx +7) Da) Use the 4-step process to find the slope of a tangent line to the graph of the function f(x) = -x2 + 3x at any point. b) Find the slope of the tangent line to the graph of the function f(x) = -3x + 4 at (-1, 7), and determine the equation of the tangent line.a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. y = (5√√x+6)x² a) Use the Product Rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. x² + 2 ( √x. +X x² 2² (1) O A. The derivative is OB. The derivative is (5√√x+6) OC. The derivative is (5√x+6) () D. The derivative is (5√x+6)x² +
- 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)A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t) = 15√t+2, find the area of the ripple as a function of time. Find the area of the ripple at t = 2. Enter the exact answer. For the number 7, you can either type pi or you can click the button with on it. Do not enter any commas in your answer.a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. F(x) = 8x* (x² – 4x) a) Use the Product Rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. A. The derivative is (x - 4x) (). O B. The derivative is 8x* ( ) + 96x 4. * () . OC. The derivative is 8x* (x - 4x) (| 4 O D. The derivative is 8x* () + (x² – 4x) (D. Click to select and enter your answer(s) and then click Check Answer. 2 parts remaining Clear All MacBook Pro
- Graph the function and the indicated tangent line. Graph f(x) = -4x2 and the tangent line to the graph at the point whose x-coordinate is -2. 10 ✔A projectile is fired from a cliff 210 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 55 feet per second. The height h of the projectile above the water is given by - 32x2 h(x) = (55)2 +x+210 where x is the horizontal distance of the projectile from the face of the cliff. Use this information to answer the following. h= 196 feet (Write a simplified fraction or an integer as your answer.) (c) At what horizontal distance from the face of the cliff will the projectile strike the water? x= feet (Round to the nearest foot as needed.) (d) Graph the function h, 0sx<210. Which of the following shows the graph of h(x)? On all graphs, the window is [0, 210] by [0, 250], with each tick mark on the X-axis representing 20, and each on the h-axis representing 50. OA. OB. OC. OD. (e) When the height of the projectile is 100 feet above the water, how far is it from the cliff? x= feet (Round to the nearest foot as needed.)Sketch the graph of the equation by making a table and plotting points. x = √y
- Which equation could represent p(x)?A Ferris wheel is 20 meters in diameter and boarded in the six o clock position from a platform that is 4 meters above the ground. The wheel completes 1 full revolution in 2 minutes. Write an equation for f(t) if f(t) gives the height of a passenger above the ground.A projectile is fired from a cliff 190 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 45 feet per second. The height h of the projectile above the water is given by - 32x? h(x) = (45)? +x+ 190 where x is the horizontal distance of the projectile from the face of the cliff. Use this information to answer the following. (a) At what horizontal distance from the face of the cliff is the height of the projectile a maximum?
