Question

Find the area of the region bounded by the tangent line to the curve f(x)=x^.5 at x=4, the curve, and the x-axis

Answer 1

i really just need help finding the tangent line's equation

Answer 2

The slope of the tangent line is f'(4)

Answer 3

ok, so how do i take that and make an equation?

Answer 4

f'(x) = .5x^(-.5)
f'(4) = .5*4^(-.5) = .5 / 2 = .25

Answer 5

the tangent has to go through the point (4, 2)

Answer 6

2 = 4*.25 + b
b = 2 - 1 = 1
the tangent line is y = .25x + 1

Answer 7

how do you know that?

Answer 8

because that's the value of f(4)

Answer 9

that it has to go throug (4, 2), i mean

Answer 10

the tangent line must go through the same point as the function

Answer 11

ohhh ok. thanks so much i understand that now

Answer 12

Integrate[.25 x + 1 - x^.5, {x, 0, 4}] = 2/3

Answer 13

ok thank you :)

Answer 14

wait wouldnt you have to set the eq's equal to each other because its not bounded by the y axis?