Question

Find the slope of the tangent line to the graph of f at the given point.

f(x) = x^2 + 5x at (4, 36)

Answer 1

That is the same as finding the derivative of the function at \(x=4\)

Answer 2

how can i solve it

Answer 3

Firstly, can you find the derivative of \(f(x)\)? :)

Answer 4

how?

Answer 5

Are you taught differentiation? :)

Answer 6

no

Answer 7

@hartnn That's interesting

Answer 8

you'll only need one formula of derivative here.
\(\large \dfrac{d}{dx}x^n = n x^{n-1}\)

Answer 9

so, can you find derivative of x^2 ?
plug in n=2 in the formula

Answer 10

@hartnn how can i find derivative of x^2 ?... Could you help me out trough

Answer 11

@hartnn Is there anyway to calculate tangent without calculus? :o

Answer 12

i don't think so
we can find the value of x for which the function is max or min, but slope of tangent.....we'll need derivative
this question does belong to derivative topic right ?
if not, then which topic ?limits?

Answer 13

Yes the topic is derivative

Answer 14

so you should have that formula which i gave you
anyways, to find derivative of x^2
you'll just have to put n=2 in that formula
what do u get ?

Answer 15

and what does d stand for

Answer 16

\(\dfrac d{dx}\) is an expression meaning "differentiate"

Answer 17

yes
dx is the change in variable 'x'
d f(x) is the change in function of x
so, df(x)/dx is the change in function, with respect to change in x
which we call as derivative of f(x)

Answer 18

so what digit is d for... i am stuck

Answer 19

\(\large \dfrac{d}{dx}x^n = n x^{n-1}\)
put n=2 there
what do u get ?

Answer 20

\[\frac{ d }{ dx }4^{2}=2(4)^{2-1}\]

Answer 21

why did u put x= 4 :O

you'll only get
d/dx (x^2) = 2x
right ?

Answer 22

yes

Answer 23

using same formula can you tell me derivative of x ?

Answer 24

hint : x means x^1, so put n=1 in that formula

Answer 25

2x

Answer 26

try again :)

Answer 27

x^2

Answer 28

2x was the derivative of x^2
to get the derivative of 'x', plug in n=1 in that formula
what u get if u put n=1 there?

Answer 29

\[\frac{ d }{ dx }x ^{1} =1x ^{1-1}\]

Answer 30

yes
1x^0
and whats x^0 =... ?

Answer 31

0

Answer 32

no...x^0 is just =1
so derivative of x just =1
got this?

Answer 33

yup at last i got it

Answer 34

good!
so now try to find the derivative of
x^2+5x ?

Answer 35

Note : constants can be taken out of the derivative
so d/dx (5x) = 5 d/dx (x)

Answer 36

oka moment

Answer 37

then

Answer 38

could you find derivative of x^2+5x ?

= derivative of x^2 + 5 derivative of x
=. ...?

Answer 39

0 right

Answer 40

no how?

we just found derivative of x^2
and derivative of x right ?

Answer 41

sory derivative of x is 1

Answer 42

yes,
and derivative of x^2 ?

Answer 43

its 1 again

Answer 44

no...
we found that derivative of x^2 =2x , right ?
by putting n=2 in the formula

Answer 45

ohh yes that right

Answer 46

could you find derivative of x^2+5x ?

= derivative of x^2 + 5 derivative of x
=. ...?

Answer 47

derivative of x^2+5x is 7x right

Answer 48

why 7x ?

Answer 49

2x + 5x = 7x

Answer 50

2x is correct
but not 5x
5 * derivative of x = 5*1 =5
got this?

Answer 51

ohh

Answer 52

because derivative of x is 1 !

Answer 53

ohh ok

Answer 54

so
derivative of x^2+5x = 2x+5
right?

Answer 55

yes

Answer 56

so we go ahead and put the value of x and solve right

Answer 57

so the slope of tangent at 4,36
is the derivative of graph at 4,36
so just put x=4 in your derivative

yes, right!

Answer 58

13 is the answer right

Answer 59

absolutely :)

Answer 60

woooo.. that was long steps for 1 question... U deserve more than medal @hartnn

Answer 61

thnxs alot @hartnn

Answer 62

don't worry for steps,
once you have enough practice, you'll be able to solve derivatives questions mentally ;)
you're welcome ^_^