Finding points on a tangent line

In summary, the problem is to find the point(s) on the graph of the function where the tangent line has a slope of -4. After deriving the function, the solution is to set the equation to the given slope and solve for the x-values. However, there was a mistake made in solving the quadratic equation, resulting in an incorrect x-value. The correct point is (0,8).
  • #1
Vandella
25
0

Homework Statement



Find the point(s) on the graph of the function at which the tangent line has the indicated slope. (If an answer does not exist, enter DNE.)

g(x) = (1/3)x^3 - (1/2)x^2 - 4x +8

mtan=-4

Homework Equations





3. The Attempt at a Solution

firstly i derived g(x) to give x^2-x-4
as tangent line = -4 substituted into equation to give x^2-x-4=-4
manipulated to get x^2-x=0
that gave me x=0 or x=-1
used those values in original function to find y values
points i obtained were (0,8) and (-1,67/6)

when i enter these with lowest x value first it says i am wrong please help
 
Physics news on Phys.org
  • #2
Since this is just a silly brainfart mistake I'm going to give you the answer, x=-1 is not a solution, you made a silly mistake when you solved the quadratic.
 
  • #3
ahhh i can't believe i missed that

thanks
 

FAQ: Finding points on a tangent line

How do you find the equation of a tangent line to a curve?

The equation of a tangent line to a curve can be found by using the derivative of the curve at the point of tangency. The slope of the tangent line will be equal to the derivative at that point. To find the y-intercept of the tangent line, substitute the coordinates of the point of tangency into the equation and solve for the y-intercept.

What is the difference between a tangent line and a secant line?

A tangent line touches a curve at only one point, while a secant line intersects the curve at two points. The slope of a tangent line is equal to the derivative of the curve, while the slope of a secant line is the change in y over the change in x between the two points of intersection. As these two points get closer together, the secant line becomes more like the tangent line.

How many points of tangency can a curve have?

A curve can have multiple points of tangency, depending on its shape. For example, a circle has an infinite number of points of tangency, while a straight line has no points of tangency.

Can a tangent line be horizontal?

Yes, a tangent line can be horizontal. This occurs when the slope of the curve at the point of tangency is equal to 0. In this case, the equation of the tangent line would simply be y = the y-coordinate of the point of tangency.

What is the significance of finding points on a tangent line?

Finding points on a tangent line allows us to approximate the behavior of a curve at a specific point. It can also help us find the slope of the curve at that point, which is useful in many applications such as optimization and curve sketching.

Similar threads

Can a Function Have Two Different Tangent Lines at the Same Point?
Replies
2
Views
1K
Quadratics Having a Common Tangent
Replies
1
Views
607
Find the two points on the curve that share a tangent line
Replies
9
Views
2K
Find the equation of the tangent plane and normal to a surface
Replies
1
Views
786
How to find the straight tangent line?
Replies
6
Views
1K
Calculating the equations for the tangent/normal lines
Replies
5
Views
2K
Find eqn for "normal" line to the tangent- folium
Replies
6
Views
1K
Solve the attached problem that involves circle and tangent
Replies
2
Views
868
Write the tangent lines to the curve
Replies
1
Views
1K
Find the equation of a tangent line to y = x^2?
Replies
11
Views
4K

Hot Threads

Recent Insights

Back
Top