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
at
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-MYMATHLAB
- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_forward5. Find the equation of the tangent linearrow_forward(VII) Find the equation of the curve for which the second derivative is 6. The curve passes through the point (P (1,2) with slope 8. Plot the curve to verify the result.arrow_forward
- Find an equation of the tangent line to the graph of the function at the given point, (a) use a graphing utility to graph the function and its tangent line at the point, and (b) use the tangent feature of a graphing utility to confirm your results y = (4x3 + 3)2, (−1, 1)arrow_forwardQuestion 6z²+4 8y³ where y(0) = 1, solve for y. You may leave your answer as an implicit function of y, if necessary. Givenarrow_forwardBy using fixed points find the roots of equation f(x) = x + 4x – 2 x, = 0 E= 0. .0001arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning