Graphing slope of function and tangent line

[john3j]

Hello,

I am new to the forum and was hoping to find someone to point me in the right direction. I will tell you the instruction to the problem and the problem itself so that you can guide me in the right direction, but am in no way asking anyone to do the work for me.

Instructions:
Use a graphing utility to find the slope of f(x) at the given point. Sketch the graph of f(x) and tangent line at the given point on your paper.

Problem:
f(x)=((4+2x)/(sqrt(x))); (16,9)

I have looked through our book and cannot find a problem like this, and I have no idea what graphing utility I am supposed to be using, or if there are any free ones available online. If anyone could tell me how to solve this, it would be greatly appreciated. Again, I am not asking for anyone to solve this for me, but another example or guidance would be greatly appreciated!

Thank you,
John

 

[wjm11]

Hello,

I am new to the forum and was hoping to find someone to point me in the right direction. I will tell you the instruction to the problem and the problem itself so that you can guide me in the right direction, but am in no way asking anyone to do the work for me.

Instructions:
Use a graphing utility to find the slope of f(x) at the given point. Sketch the graph of f(x) and tangent line at the given point on your paper.

Problem:
f(x)=((4+2x)/(sqrt(x))); (16,9)

I have looked through our book and cannot find a problem like this, and I have no idea what graphing utility I am supposed to be using, or if there are any free ones available online. If anyone could tell me how to solve this, it would be greatly appreciated. Again, I am not asking for anyone to solve this for me, but another example or guidance would be greatly appreciated!

Thank you,
John

You can either use your own graphing calculator or simply type the function into a Google search to see the graph. Copy the graph onto paper and sketch (estimate) the tangent line. The problem does not seem to be asking for the exact solution for the tangent line. If you want the exact slope of the line, find the derivative of the original function and plug in 16 for x.

 

[mmm4444bot]

If you use Google to display the graph, click-and-drag the graph to the vicinity of x=16.

The behavior of function f should appear almost linear, in that vicinity.

Note that moving the mouse pointer provides a trace along the graph, with coordinates displayed.

Hence, another way to estimate the slope at x=16 would be to use some appropriate coordinates from both sides in the slope formula.

Cheers :cool: