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A.Find the slope of the tangent line to the graph of f at the given point.
A.Find the slope-intercept equation of the tangent line to the graph of f at the given point.

- anonymous

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- welshfella

find the derivative
f(x) = 4x + 2
can you find f'(x)?

- anonymous

-1/2+x/4

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- anonymous

no the derivative of that is 4

- welshfella

yes thats right so the slope is - at every point on the graph as its a straight line

- welshfella

* slope is 4

- welshfella

the second function is:-
f(x) = x^(1/2)
can you find the derivative of this one?

- anonymous

x^-1/2/2

- welshfella

|dw:1435264790652:dw|

- welshfella

so to find the slope at (16,4) plug x = 16 into the the above value for f'(x)

- welshfella

then use the general form
y-y1 = m(x-x1)
and plug in slope m and the point (x1,y1) will be (16,4)

- anonymous

for the first step is it 2

- welshfella

1 / 2*x(1/2) = 1 / 2* (16)^1/2 = 1/ 2*4 = 1/8

- welshfella

so m = 1/8

- anonymous

im lost. I don't understand this at all.

- welshfella

m stands for the slope in the formula
the slope is given by the derivative of sqrt x - and is 1 / 2* x (1/2) o r 1 / 2 sqrtx
here x = 16 ( point is (16/4)
so m = 1 / 2 sqrt16 = 1 / 2*4 = 1/8

- anonymous

ok but its two parts to the problem that's the answer to both?

- anonymous

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- anonymous

@LynFran

- LynFran

ok what exactly u dont understand here?

- anonymous

i dont understand the problem or the question this whole thing confuses me.

- LynFran

ok lets go through this step by step from the beginning ok

- anonymous

ok

- LynFran

first of all the slope of a tangent line is the gradient of that line ok

- anonymous

what is a gradient

- LynFran

now to find the slope of the tangent line is y/x...|dw:1435279410553:dw|

- LynFran

The Gradient (also called Slope) of a straight line shows how steep a straight line is.

- anonymous

the question has two parts is 4 the answer for both

- LynFran

|dw:1435279812417:dw|

- LynFran

4 is just the slope of the tangent line we have to find the slope intercept equation at the given point ok to complete this question ok

- anonymous

ok whats the next step

- LynFran

|dw:1435280154077:dw|

- LynFran

what equation u get??

- anonymous

y=4x+2

- LynFran

correct

- anonymous

ok so thats the second part to the first question?

- LynFran

we just did 2nd question and yes that was this part; .Find the slope-intercept equation of the tangent line to the graph of f at the given point.

- anonymous

ok so 1.4 and 2. y=4x+2

- LynFran

yes Find the slope of the tangent line to the graph of f at the given point. is 4

- LynFran

for that question

- anonymous

ok got it

- LynFran

Did u do the other question?

- anonymous

can you help me with that one too?

- LynFran

ok

- LynFran

|dw:1435281016248:dw|

- LynFran

|dw:1435281095053:dw|

- LynFran

now to take the derivative of it we get|dw:1435281258598:dw|

- LynFran

|dw:1435281332523:dw|

- LynFran

|dw:1435281411275:dw|

- anonymous

ok im with you, so whats next

- LynFran

well we have to plug in the value of x into the derivative we just found

- LynFran

(16,4) and x=16 there ok so.. plug it into the derivative and let me know what u get

- LynFran

|dw:1435282159975:dw|

- anonymous

ok so when i plug in 16 and solve to find the derivative i get 0

- LynFran

no u cant get 0 lets work it together

- anonymous

ok

- LynFran

|dw:1435282473866:dw|

- LynFran

so 1/8 is this part Find the slope of the tangent line to the graph of f at the given point.

- anonymous

ok

- LynFran

so can u find this part now .Find the slope-intercept equation of the tangent line to the graph of f at the given point.
|dw:1435282844490:dw|

- anonymous

4-y1=1/8(16-x1)

- LynFran

no we leave the y and x term alone and uses the y1 and x1

- LynFran

|dw:1435283138396:dw|

- anonymous

ok y-4=1/8(x-16)

- LynFran

correct now the next step is to multiply out the bracket

- anonymous

y-4=1/8x -2

- LynFran

good next step is to bring the -4 over the equal sign ...remember when we bring a # over the equal sign , the sign of the # changes

- anonymous

y=1/8x+2

- LynFran

yes and u have officially completed the question ok now i would like to share this site with u it was very useful to me so https://www.symbolab.com/solver/calculus-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(%5Csqrt%7Bx%7D%5Cright)/?origin=button

- anonymous

ok thank You so much for your help.

- LynFran

ur welcome

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