Question

If f(x)=x^4+5e^x, find f′(5).
Use this to find the equation of the tangent line to the curve y=x^4+5e^x at the point (a,f(a)) when a=5. The equation of this tangent line can be written in the form y=mx+b where m is:
4 5^3+5 e^5
and where b is: ?

Answer 1

@Chlorophyll to find b you take y-y1=m(x-x1)

Answer 2

Yup, tangent line is actually a straight line!

Answer 3

this gives you (y-625+5 e^5)=4 5^3+5 e^5(x-5)

Answer 4

lol wouldn't surprise me at all

Answer 5

f (5) = 5^4 + 5 e^5
= 625 + 5 e^5

Answer 6

ah ok i see what i did there

Answer 7

idk what im doing wrong but must be typing something in wrong

Answer 8

(1000+5e^5)(-5)=(-5000-25 e^5)

Answer 9

(-5000-25 e^5)+625+5e^5=-4375-20 e^5

Answer 10

and for some reason it doesnt like that

Answer 11

nope this program is pretty stupid

Answer 12

slope m = f'(5) = 4*5³+5 e^5
= 500 + 5e^5 = 5( 100 + e^5)

Answer 13

ok there we go that worked

Answer 14

f (5) = 5^4 + 5 e^5
=> y = 500 + 5e^5 ( x - 5) + 625 + 5 e^5
Thus b = ...

Answer 15

-1875-20 e^5
hey i give you props for doing all of this in your head i consider myself pretty good at doing math in my head, and cant even start to think about this stuff

Answer 16

either way its alot better than i could do. how much paper do you go through in a night?

Answer 17

ya just messed up the slope but other then that i get the concept well :)

Answer 18

yup thanks for being so patient with me calc is kicking my but

Answer 19

ya i need to become more organised and hopefully il be ready for calc next time i take it

Answer 20

no otherwise i would be doing it all, i hate collage

Answer 21

that i should my biggest problem is that i never took pre calc or anything in hs and now im in calc and my teacher doesnt teach anything

Answer 22

yes but i tested into calc and its the lowest class that my major accepts as credit

Answer 23

Now, your life is engaged with the OS site forever :P