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

-1/2+x/4

no the derivative of that is 4

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

* slope is 4

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

x^-1/2/2

|dw:1435264790652:dw|

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

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

for the first step is it 2

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

so m = 1/8

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

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

ok what exactly u dont understand here?

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

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

ok

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

what is a gradient

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

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

the question has two parts is 4 the answer for both

|dw:1435279812417:dw|

ok whats the next step

|dw:1435280154077:dw|

what equation u get??

y=4x+2

correct

ok so thats the second part to the first question?

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

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

for that question

ok got it

Did u do the other question?

can you help me with that one too?

ok

|dw:1435281016248:dw|

|dw:1435281095053:dw|

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

|dw:1435281332523:dw|

|dw:1435281411275:dw|

ok im with you, so whats next

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

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

|dw:1435282159975:dw|

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

no u cant get 0 lets work it together

ok

|dw:1435282473866:dw|

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

ok

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

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

|dw:1435283138396:dw|

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

correct now the next step is to multiply out the bracket

y-4=1/8x -2

y=1/8x+2

ok thank You so much for your help.

ur welcome