Is Y=23x+18 the Correct Equation for the Tangent Line at X=2?

[chjopl]

Find the equation of the tangent line at x=2
F(X)=2x+7x(e^(x-2))

I know you put 2 into find the y intercept and you take the derivative to find the slope. I get 2+(7e^(-2)x + 7e^-2)e^2 for my derivative and y=23x+18 as my answer and i know that is not correct.

 

[shmoe]

You derivative looks off. Remember,

[tex]\frac{d}{dx}e^{x-2}=e^{x-2}\frac{d}{dx}(x-2)=e^{x-2}(1)=e^{x-2}[/tex]

and apply the product rule carefully!


edit-ahh, Galileo is right, your slope is fine. Your posted derivative may be a casualty of ascii.

 

[Galileo]

You got the slope right. So y=23x+b. Now use the fact that the line passes through the point (2,f(2)) to find b.

 

[dextercioby]

Find the equation of the tangent line at x=2
F(X)=2x+7x(e^(x-2))

I know you put 2 into find the y intercept and you take the derivative to find the slope. I get 2+(7e^(-2)x + 7e^-2)e^2 for my derivative and y=23x+18 as my answer and i know that is not correct.

The derivative should be:
[tex] f'(x)=2+[7\exp({-2})](\exp{x}+x\exp{x) [/tex]
Insert 2 to find the slope.It's 23.
Compute f(2).It's 18.With the last 2 numbers,u should be able to find the equation for the tangent line.

We're just like eagles when it comes to simple problems.Three almost identical posts at the same time...

 

[chjopl]

so was y=23x+18 correct?

 

[dextercioby]

so was y=23x+18 correct?

Obviously not,try to follow my post correctly.It's easy maths,after all.

 

[HallsofIvy]

so was y=23x+18 correct?

What is 23(2)+ 18?