The problem involves finding the line tangent to the curve defined by the function f(x) = 0.5x² + 3x - 1, which is parallel to the line g(x) = x/2 + 0.5. The discussion centers around the relationship between the slopes of the tangent line and the given line.
The discussion has progressed with participants identifying the slope of the tangent line and attempting to find the corresponding x-value where the derivative equals that slope. Some participants have noted arithmetic mistakes and are working towards correcting them.
There are indications of confusion regarding arithmetic calculations, and the need to adhere to the problem's requirements regarding derivatives and tangent lines is emphasized.
bubblescript said:Homework Statement
Find the line tangent to the curve f(x)=0.5x2+3x-1 which is parallel to the line g(x)=x/2+0.5
Homework Equations
f'(x)=x+3
The Attempt at a Solution
I know it involves taking the derivative of f(x) and using it somehow, but I don't know where to go from there.
bubblescript said:Both lines will need to have the same slope, 1/2.
bubblescript said:The slope is 1/2 when f'(x)=1/2:
1/2=x+3
x=5/2
bubblescript said:Yes caught the mistake.
So using -5/2 on f(x) gets f(-5/2)=-43/8, which means a point on the line is (-5/2, -43/8).
If the line is of the form y=1/2*x+b, we substitute the point for x and y:
-43/8=1/2*-5/2+b
b=-33/8
The line is: y=1/2*x-33/8