In Exercises 33-40, find an equation of the tangent line to the graph
at the given
Example 4
Finding the Equation of Tangent Line at Given
Find the point-slope equation of the tangent line to the graph of
Solution
In this problem, we are given a point on the tangent line, but only its first coordinate
Since the point is on the graph
-value into
Thus,
is the point on the graph and the tangent line. Next, we find the slope of the tangent line. For this purpose, we compute
by using the power rule:
The slope tangent line when
is
In the
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Calculus & Its Applications (14th Edition)
- Find the general solution of the separable equation. Express the solution explicitly as a function of the independent variable.arrow_forwardFind the slope and equation of the tangent line to the graph of the equation at a given point. Show your solution. 1. y = 2x² + 4x at point (-2,0)arrow_forwardFind equations of the tangent lines to the curve y=(5ln(x)) / x at the points (1,0) and (e, 5/e) at the point (1,0) y= at the point (e, 5/e) y= Illustrate by graphing the curve and its tangent lines.arrow_forward
- Based on your initial ideas, give five different examples wherein you can apply the concept of derivatives. Examples: Calculating profit and loss in business using graph Deriving equations in physics such as speed and acceleration.arrow_forwardThe rate of increase of COVID-19 infection is directly proportional to the number of people infected and to the number people not yet infected. An isolated remote barangay of population 10,000 records its first case on June 15, 2020. After two days, 100 people are infected. Develop a model that predicts the number of COVID-19 cases in the barangay. How long will it take for 90% of the population to be infected? Assume that the virus persists in the person infected.arrow_forwardBased on your initial ideas, give five different examples wherein you can apply the concept of derivatives. Example: Calculating profit and loss in business using graph Deriving equations in physics such as speed and acceleration.arrow_forward
- calculus Find the equation of the tangent line to the graph of f(x) = 4 - x2 at point (1,3).arrow_forwardA. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of the slope of the secant line through the point B. Find the equation of the tangent line to the curve at (2, -4)arrow_forwardFinding F of G times X of the equations?arrow_forward
- Solve for the equation of the tangent line to the curve y=3x2-4 that is parallel to the line 3x+y=4 using the slope of tangentline’s (mT) definition. Then, solve for the equation of the normal line too.arrow_forwardDetermine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The tangent line approximation at any point for any linear equation is the linear equation itself.arrow_forwardLine AD and line BC intersect at point F solve for x.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage