Question

Find an equation for the line tangent to the graph of:

f(x)=6xe^x

at the point (a,f(a)) for a =2

y= ?

Answer 1

did you take the derivative?

Answer 2

I was doing implicit differentiation

Answer 3

product rule you mean?

Answer 4

implicit differentiation is just for when your function is a function of x and also y

Answer 5

ohh

Answer 6

So i take the derivative?

Answer 7

yes, the derivative tells you the slope of the tangent line (for any x)

Answer 8

tell me what you get for the derivative...

Answer 9

f(x)'=6xe^x=6e^x

Answer 10

good

Answer 11

oops that was a plus

Answer 12

I figured:)

Answer 13

f(x)'=6xe^x+6e^x

Answer 14

so we want the slope at x=2

Answer 15

18e^2

Answer 16

is m the slope use in y=mx+b with x=2 and y = 6*(2)*e^2
to find b

Answer 17

you lost me

Answer 18

which part?

Answer 19

you found the slope of any tangent line: 6xe^x+6e^x
the slope of the tangent line for x=2 is: 6*2*e^2 + 6*e^2

Answer 20

18e^2

Answer 21

SO that is the slope when x=2

Answer 22

yep;)

Answer 23

Ohh haha

Answer 24

we can use that to find the equation of the tangent line that goes through that point...

Answer 25

y = 18*e^2 *x +b

Answer 26

and the point we're looking at is (2, 6*2*e^2)

Answer 27

sub.s those points in for x and y, and solve for b:)

Answer 28

OKay cool thank you

Answer 29

ok? all good? any questions?

Answer 30

Sure!