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Calculus 1 Problem - Need Help!!

S

Stokes

Senior member
I'm unable to figure out this extra credit problem for my Calc class and if I can get some help, i would really appreciate anything anyone can do for me!

Here is the problem:

Find the values of x, for which the line tangent to the graph of f(x)=(1/3)x^3 - (3/2)x^2 - 11x + 4 is parallel to the line passing through the points (1,2) and (3,0).

I understand how to find the slope-intercept form of an eqution to the line tangent to the graph, but I don't know where do start here or where what I know goes into this problem?

Any math genius out there help me please?
 
First you find the slope the tangent. Since a line between (1,2) and (3,0) is parallel with the tanget, that means they have the same slope. So the slope of the tangent line is (0-2)/(3-1) or -1. Now take the derivate of f(x), which is x^2 - 3x -11. Set that equal to -1 and solve for x. x^2 - 3x -11 = -1. Solving for x you get, x=-2 and x=5. Now plug in one of the points into f(x), to find a point. Plug that point and the slope of the tangent line into y=mx + b to find your y-int. Once you find that, you are good to go.
 
So, you can find the equation of the line through the two points that you are given. What do the equations of the two lines have to have in common in order to be considered parallel? After you answer that question, use that as a hint to tell you what tool you might need to use in order to start getting the answer to the problem.

-Tom
 
Find the slope of the parallel line. Take the derivative of f(x). Plug slope of line into f'(x) to find what x values have tangent line slopes that are the same as between points (1,2) and (3,0)
 
thanks everyone for your help, I think I got the correct answer from the guidelines.

I really appreciate it!
 
Wow, the regular homework questions I assign are harder than that...

Consider yourself lucky!
 
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