Question [Help]

[Abdullah]

View attachment 13717

39) F(x) = 2x + 4^-x . .............. edited

Show that the tangent to the curve with y = F(x) at the point at (-1,y) is

15*ln(2) * x + 2 * y + 15*ln(2) - 9 = 0

 

[Deleted member 4993]

View attachment 13717

F(x) = 2x + 4^-x . .............. edited

Show that the tangent to the curve with y = F(x) at the point at (-1,y) is

15*ln(2) * x + 2 * y + 15*ln(2) - 9 = 0

Please follow the rules of posting at this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.

Hint: Calculate F'(x)

 

[pka]

View attachment 13718

F(x) = 2x + 4-x . Show that the tangent to the curve with y = F(x) at the point at (-1,y) is

Mr. Khan, as I read the function it is \(\displaystyle f(x)=2x+4^{-x}\). Otherwise, there is no way \(\displaystyle \log(2)\) into the question.
Then \(\displaystyle f'(x)=2-4^{-x}\log(4)\) note that \(\displaystyle f(-1)=2~\&~f'(-1)=2-8\log(2)\)

 

[Deleted member 4993]

Mr. Khan, as I read the function it is \(\displaystyle f(x)=2x+4^{-x}\). Otherwise, there is no way \(\displaystyle \log(2)\) into the question.
Then \(\displaystyle f'(x)=2-4^{-x}\log(4)\) note that \(\displaystyle f(-1)=2~\&~f'(-1)=2-8\log(2)\)

You are correct - I just forgot to put the super-script.

I fixed it. Thank

 

[pka]

F(x) = 2x + 4^-x . .............. edited
Show that the tangent to the curve with y = F(x) at the point at (-1,y) is
15*ln(2) * x + 2 * y + 15*ln(2) - 9 = 0

There is no way that I can see that could be correct.

 

[Abdullah]

There is no way that I can see that could be correct.

You are right, I managed to figure it out. The textbook was wrong the question was f(x) = 2^ x + 4^-x and it would give you the correct answer using this.