y=13x46x2 + 1; (-1, 8) (a) Find an equation of the tangent line to the graph of the function at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of a graphing utility to confirm your results. O-2.0 -1.5 -1.0 -0.5 Χ y 30年 20 25 20 -1.4 -1.2 -1.0 -0.8 0.6 -0.4 -0.2 -20 15 -40 10 5 -60 -80 x -100 y y x -1.4 1.2 -1.0 -0.8 0.6 0.4 -0.2 30 -20 25 20 -40 15 -60 10 5 -80 -2.0 -1.5 -1.0 -100 -0.5 ×
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- solve for y to determine if y is a function of x. If it is, express it using function notation. What is the domain? x+y^2=2Sketch the graph of the functionFind equations of the tangent line and the normal line to the graph of the function f(x) = 5x² + 8 at the point (-3,53). %3D (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equations in %3D terms of y and x.) tangent line equation: normal line equation: Select the image containing the graph of the function, the tangent line, and the normal line at the indicated point on the same set of coordinate axes.
- SOLVE STEP BY STEP IN DIGITAL FORMAT 9. For the function f(x) = x^3 - 3x^2 - 13x - 15. Calculate the roots of the function f(x), find the maximum and minimum points of the function f(x), determine the inflection point of the function f(x), find the intervals where the function is concave up and concave down, calculate the intervals of increase and decrease of the function and graph.Find all values of a where the graph of f(x) = 2x³ - 39x² + 240z - 5 has a horizontal tangent line. Point(s): Use comma(,) to seperate multiple points. Ex: (1, 2), (2, 3)Sketch the graph of f(x)= square root(-1-x) by hand, without calculator
- The graph below shows the velocity v in feet per second of a small rocket that was fired from the top of a tower at time t = 0 (t in seconds). The rocket accelerated with constant upward acceleration until its fuel was expended, then fell back to the ground at the foot of the tower. The entire flight lasted 14 seconds. 4. (4,96) t (seconds) (14,-224) (a) What was the acceleration of the rocket while its fueled lasted? (b) How long was the rocket rising? (c) What distance did the rocket travel during the time it was rising? (d) How high was the tower from which the rocket was fired? v (ft/sec)A water feature on a fountain follows a parabolic path and is represented by the function f(x) = -x(x – 8), which models the vertical distance as a function of the horizontal distance in feet. According to the graph of the function, the greatest height the water reaches is feet?What is the slope of the tangent line to the function: f (x) = In (2 x² + 2 x – 11) at the point P(2,0)? m = Find the equation of the tangent line to the point P(2,0).The answer should be written in slope-intercept form. y = symbolic formatting help