Question

Calculus-Tangent Line
For what value(s) of x will be the slope of the tangent line to the graph of h(x)=4 times square root (x) be -2? Find the equation of the line tangent to h(x) at this/these x-values. Show your work.

Answer 1

\[h(x)=4\sqrt{x}\]

Answer 2

I took the derivative of h(x) and set it equal to -2 and found x=1

Answer 3

\[h'(x)=\frac{ 2 }{ \sqrt{x} }\]

Answer 4

I found h'(1)=2 my point is (1,4)
My tangent line is y-4=2(x-1)

Answer 5

When I went to check my work, I am not seeing the slope of the tangent line -2 so what am I overlooking?

Answer 6

Let's take another stab at finding the derivative of\[h(x)=4\sqrt{x}.\]I would first write this function as\[h(x)=4\sqrt{x}=4x ^{1/2}=4(1/2)x ^{(1/2)-1}.\]

Answer 7

Please finish finding the derivative, and then compare your result with your previous one.

Answer 8

\[h'(x)=2x ^{-1/2}\]

Answer 9

I thought I did finish finding the derivative above about 3 steps back

Answer 10

\[h'(x)=\frac{ 2 }{ \sqrt{x}}\]

Answer 11

Yes, which is precisely the same as what you got, except for format.

The problem statement says that this slope is equal to -2. Mind solving for x again?
Would like to see your work.

Answer 12

no I don't mind. Please give me a moment to type it in

Answer 13

\[\frac{ 2 }{ \sqrt{x} }=-2\]

Answer 14

I cross multiplied

Answer 15

Is there a solution?

Answer 16

\[-2\sqrt{x}=2\]
divided both sides by -2
\[\sqrt{x}=-1\]
squared both sides
\[x=1\]

Answer 17

Sticky. Supposing that you now substitute x=1 into \[\frac{ 2 }{ \sqrt{x} }=-2\]...would the result be true or false?

Answer 18

False, ok they got me..........

Answer 19

I also, know the parent function is the square root function which is increasing

Answer 20

It's a little hard to get 2/Sqrt(1) to equal -2, isn't it?

Might be worth actually graphing h(x)=4Sqrt(x).

Answer 21

yes actually I did graph it and realized that the slope could not be -2 anywhere. I just did not think the question was meant to trick me. Thanks :)

Answer 22

I think this graph will immediately tell you why the slope of this function h)x) is not going to be -2. You're welcome!

Answer 23

I thought I had done something wrong.

Answer 24

Another great reason to learn your parent functions.....

Answer 25

That's always a problem for us bright people, isn't it? We hate to be wrong.

Also a good idea to be thoroughly familiar with the shapes of the graphs of common functions, including \[\sqrt{x}, x,x^2, \sin x, \cos x, and so on.\]

Answer 26

yes thanks once again. :)

Answer 27

You're welcome! Bye.