Tangent lines Find an equation of the line tangent to the graph of f at the given point.
33.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Glencoe Math Accelerated, Student Edition
Calculus & Its Applications (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=3sin(t/4), where y is the displacement in feet and t is the time in seconds. Complete the table Use the table feature of a graphing utility to determine when the displacement is maximum. Use the table feature of the graphing utility to approximate the time t (0 < t < 8) when the weight reaches equilibrium.arrow_forwardDerivatives from graphs Use the figure to find the followingderivatives.arrow_forwardSecond derivatives Find y″ for the following functions. y = 1/2 ex cos xarrow_forward
- Find the values of x where the tangent line to the graph of f(x)=1x is parallel to the line y=-6x+3.Give exact answers (not decimal approximations).(Tip: To enter a, type either sqrt(a) or a^(1/2).)The greater solution is x = and lesser solution is x =arrow_forwardQ-2))))Using the appropriate 3-Point and 5-Point Formulas with the values given in the table above, using different values of h and f'(46)Make an approximation of the derivative.arrow_forwardLocations of tangent linesa. For what values of x does g(x) = x - sin x have a horizontaltangent line?b. For what values of x does g(x) = x - sin x have a slope of 1?arrow_forward
- a. Find the local extrema of each function on the given interval,and say where they occur.b. Graph the function and its derivative together. Comment onthe behavior of ƒ in relation to the signs and values of ƒ′.59. ƒ(x) = sin x-cosx, 0 ≤ x ≤2Πarrow_forwardDerivatives from a table Use the table to find the followingderivatives.arrow_forwardInconclusive tests Show that the Second Derivative Test is inconclusive when applied to the following functions at (0, 0). Describe the behavior of the function at (0, 0). ƒ(x, y) = sin (x2y2)arrow_forward
- a. Find the local extrema of each function on the given interval,and say where they occur.b. Graph the function and its derivative together. Comment onthe behavior of ƒ in relation to the signs and values of ƒ′.59. ƒ(x) = sin x+sqrrt(3)cosx, 0 ≤ x ≤2Πarrow_forwarda. Find the local extrema of each function on the given interval,and say where they occur.b. Graph the function and its derivative together. Comment onthe behavior of ƒ in relation to the signs and values of ƒ′.59. ƒ(x) = sin 2x, 0 ≤ x ≤Πarrow_forward2)Find the first and second derivative of the function for x greater than zero. f(x)= ln(x) f '(x) = f ''(x) = i)Is the first derivative positive or negative? ii)Is the second derivative positive or negative? iii)Which of the following describes the graph of y = ln x? Decreasing and concave down Increasing and concave up Decreasing and concave up Increasing and concave downarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning