12. For the following function find the derivative, factor and simplify and find where the tangent...
5x + 1 Use the definition of the derivative to find the derivative of the function f(x) = *-*2. Then find all x-values (if any) where the tangent line is horizontal. If the tangent line is horizontal for all X, write R for your answer. If the tangent line is never horizontal, write None for your answer Answer 3 Points Keypad 11 1'(x) = 2 Tangent is horizontal at x = Prev Nex If f(3) = -1, f(3) = 17,...
Find the derivative of the function. F(x) = x – 5x V x √x (a) Simplify the function to the point where you will not need the Product or Quotient Rule (b) Use the part a), find the derivative of the function. F'(x) =
Use first derivative analysis (no calculators) to graph each function. (By first derivative analysis we mean the following as demonstrated in class: find critical values indicate whether the first derivative is 0 (producing a horizontal tangent) or undefined (producing sharp corner or vertical tangent) at each critical value o o o show tables of intervals where f increases or decreases and thus whether critical values correspond to a local maximum, local minimum, or neither). x) (4-x2) Use first derivative analysis...
Use the fact that the derivative of the function g(x) = /x is g'(x) = 2/x to find the equation of the tangent line to the graph of g(x) at the point x = 1. %3D The equation of the tangent line is y = (Simplify your answer.) is f'(x) = Use the fact that the derivative of the function f(x) = to find the equation of the tangent line to the graph of f(x) at the point x= -...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
14. x Find the derivative of the function using the definition f(x) = x + 3 15. The equation of motion of a particle is s = p - 27t, where s is in meters and t is in seconds. (Assume 10.) (a) Find the velocity and acceleration as functions of t. (b) Find the acceleration after 4 s. (c) (c) Find the acceleration when the velocity is 0. 16. Find the points on the curve y = 2x3 +...
For the function, find the points on the graph at which the tangent line is horizontal y=x +5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The point(s) at which the tangent line is horizontal isare) (Type an ordered pair Use a comma to separate answers as needed.) OB. The tangent line is horizontal at all points of the graph. OC. There are no points on the graph where...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks 6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
3.1.37 a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to the graph off at (a f(a) for the given value of a. c. Graph fand the tangent line. f(x) = 2x²+x-1, a=-1 a.f'(x)=