What are the equations of the tangent lines to both functions?

  • Thread starter Thread starter teken894
  • Start date Start date
  • Tags Tags
    Functions Tangent
Click For Summary
SUMMARY

The discussion focuses on finding the equations of the tangent lines to the functions f(x) = x² and g(x) = -x² + 6x - 5. The user initially attempted to equate the derivatives f'(x) = 2x and g'(x) = -2x + 6 to find a common slope, resulting in x = 1.5 and a slope of 3. However, this approach is flawed as it only identifies a point where the slopes are equal, not the tangent lines. The correct tangent lines are given as y = 2x - 1 and y = 4x - 4, derived by solving for the intersection points of the lines with each curve.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with quadratic functions and their properties
  • Knowledge of solving systems of equations
  • Ability to analyze points of intersection between curves
NEXT STEPS
  • Study the method of finding tangent lines to curves using derivatives
  • Learn about the geometric interpretation of derivatives in calculus
  • Explore solving quadratic equations and their graphical representations
  • Investigate the concept of points of tangency and their significance in calculus
USEFUL FOR

Students studying calculus, particularly those focusing on derivatives and tangent lines, as well as educators looking for examples of solving tangent line problems.

teken894
Messages
25
Reaction score
0
Here's a question from my Calc HW andI believe my approach is flawed...

Two functions
f(x) = x^2
g(x) = -x^2 + 6x -5

Find the two lines tangent to both functions


I thought I could find the slope where f' and g' are equal so I did:

f'(x) = 2x
g'(x) = -2x + 6
2x = -2x +6
x = 1.5
slope = 2(1.5) = 3

BUT that slope doesn't work as this simply finds an x on the two graphs where the two graphs have the same slope.


Help me please!

THE given answers are
y=2x-1
y=4x-4
 
Physics news on Phys.org
Assume the line of tangency is y = mx +c.

Solve to find the point of intersection of y=mx + c with each of the two curves.

Keep in mind that there is only one point of intersection (with each curve) and not two x-values.
 

Similar threads

Can a Function Have Two Different Tangent Lines at the Same Point?
  • · Replies 2 ·
Replies
2
Views
2K
Quadratics Having a Common Tangent
  • · Replies 1 ·
Replies
1
Views
1K
At what ##x## value is the tangent equally inclined to the given curve?
  • · Replies 5 ·
Replies
5
Views
1K
Find the equation of a tangent line to y = x^2?
  • · Replies 11 ·
Replies
11
Views
5K
Can this function still be a constant function?
  • · Replies 11 ·
Replies
11
Views
2K
Write the tangent lines to the curve
  • · Replies 1 ·
Replies
1
Views
1K
Find g(x)/h(y) for a given F(x,y)
  • · Replies 3 ·
Replies
3
Views
1K
Verify Green's Theorem in the given problem
  • · Replies 10 ·
Replies
10
Views
2K
Evaluating scalar products of two functions
  • · Replies 1 ·
Replies
1
Views
2K
Can you clarify your understanding for parts (a) and (b)?
  • · Replies 11 ·
Replies
11
Views
2K