How do I find the x values at which the tangents to the graphs f(x)=2x^2 and g(x)=x^3 have the same slope?
f'(x) = 4 x
g'(x) = 3 x^2
when does 4x = 3 x^2 ?
3 x^2 - 4 x = 0
x (3x -4) = 0
x = 0 and x = 4/3
Assuming you are looking for the same value of x at which both tangents are parallel.
Take derivative of each, equate and solve for x.
f'(x)=4x
g'(x)=3x²
Equate and solve to get
x=0 or x=4/3
See:
http://img855.imageshack.us/i/1299374046.png/
To find the x-values at which the tangents to the graphs of f(x) = 2x^2 and g(x) = x^3 have the same slope, we need to determine the slope of the tangent lines for each function and set them equal to each other.
Step 1: Find the derivative of both functions:
The derivative of f(x) = 2x^2 is given by f'(x) = 4x.
The derivative of g(x) = x^3 is given by g'(x) = 3x^2.
Step 2: Set the derivative of both functions equal to each other:
4x = 3x^2
Step 3: Rearrange the equation and solve for x:
3x^2 - 4x = 0
x(3x - 4) = 0
Setting each factor equal to zero and solving for x give two possible x-values: x = 0 and x = 4/3 (or 1.33).
Therefore, the tangents to the graphs intersect at x = 0 and x = 4/3, meaning they have the same slope at those points.