Question

Find the equation of the line tangent to the function f(x)=5x^2 at x =10.

*not toooo sure how to do this, but would I just be subbing in 10 for x?

f(1)=5(10)^2
=5(100) =500?

or is it something else? please explain! thanks :)

Answer 1

Find the slope first. Do you know how to do that?

Answer 2

y2-y1/x2-x1 ?

or would i be subbing the x value into a y=mx+b format?

haha not sure in this scenario!

Answer 3

What class are you in right now?

Answer 4

calculus :)

Answer 5

Use a calculus concept you learned not too long ago :)

Answer 6

okay.. ermm am i using this?

lim f(a+h)-f(a)
h->0 ___________
h
? :/

Answer 7

it works, or u cud use the formula directly :

slope = derivative

derivative of \(\large x^n = nx^{n-1}\)

Answer 8

ohh okay :)

how would i use that here?

would n=5

and x=10?

Answer 9

slope of \(x^2\) at any point (x, y) = derivative of \(\large x^2 = 2x^{2-1} = 2x\)

Answer 10

since 5 is a constant, u can pull it out.

\(\large \frac{d}{dx}(5x^2) = 5*\frac{d}{dx}(x^2) = 5*2x = 10x\)

Answer 11

familiar wid this d/dx notation ?

Answer 12

ahh okay, yes looks familiar :)

Answer 13

good :)

so, slope of 5x^2 at any point (x, y) is 10x.

Answer 14

so then now you just end up with 10(10)=100?

and also just making sure... d=derivative right?

Answer 15

yes, and yes.

so u have these at hand :
slope, m = 100
point = (10, ??)

u can write the equation of line ?

Answer 16

ah okay :)

umm was that from subbing in earlier? so y=500

y=mx+b

slope = 2(10)=20

500=20(10)+b

500=200+b

subtract 200 from both sides

300=b

y=20x+300 ?

Answer 17

slope = 100 right ?
lol how come it bacame 20 all off sudden :o

Answer 18

haha ooops!

ermm so is it 500=100(10)+b

-500 =b?

y=100x-500?

Answer 19

looks good !!

Answer 20

okay awesome!! thank you :)

Answer 21

np... u wlc :)