Help needed, expon and log functions (1 Viewer)

[RHINO7]

I can't work out these questions=

i)Find the gradient of the tangent to the curve y=4e^x at the point where x=1.6, correct to 2 decimal places.


ii)Find the equation of the tangent to the curve y=-e^x at the point (1,-e)


iii)Find the first and second derivatives of y= 7e^x. Hence show that the second derivative = y

 

[jb_nc]

d(e^x)/dx = e^x

No joke that's all you ned for that question.

 

[ellen.louise]

I can't work out these questions=

i)Find the gradient of the tangent to the curve y=4e^x at the point where x=1.6, correct to 2 decimal places.


ii)Find the equation of the tangent to the curve y=-e^x at the point (1,-e)


iii)Find the first and second derivatives of y= 7e^x. Hence show that the second derivative = y

i) y=4e^x
y'=4e^x
m of tan (x=1.6) = 4e^1.6

y-4e^1.6= 4e^1.6(x-1.6)
go from there...

amirite?

iii) y=7e^x
y'=7e^x ??? is there something i am missing here? this seems too easy. i know it works for just e^x, does it work for this too???

 

[jb_nc]

they meant for (iii) that d^2y/dx^2 = y = 7e^x which it does. I have a feeling the OP is going to feel pretty stupid for not being able to do these.

 

[RHINO7]

yeah thanks, what about the second question

 

[ellen.louise]

they meant for (iii) that d^2y/dx^2 = y = 7e^x which it does. I have a feeling the OP is going to feel pretty stupid for not being able to do these.

uh huh!

 

[ellen.louise]

I can't work out these questions=

i)Find the gradient of the tangent to the curve y=4e^x at the point where x=1.6, correct to 2 decimal places.


ii)Find the equation of the tangent to the curve y=-e^x at the point (1,-e)


iii)Find the first and second derivatives of y= 7e^x. Hence show that the second derivative = y

ii)

y'= -e^x
m of tan = -e

y+e=-e(x-1)

 

[cl3nta]

jb_nc is right but here are the solutions anyways

i)
dy/dx=4e^x
at x=1.6, dy/dx=4e^1.6 = gradient

ii)
dy/dx=-e^x
at x=1, m=-e
therefore the equation is:
y+e=-e(x-1)
y=-ex

iii)
y=7e^x
dy/dx=7e^x
d^2y/dx^2=7e^x
From above, d^2y/dx^2=y=7e^x QED.

Hope that helps wait till you get to integrals

 

[cl3nta]

wow so many posts between when I read the questions to when I posted ><

 

[RHINO7]

Thanks mate