Question

find the equation of the tangent line to the curve when x has the given value.
f(x) = sqrt (x) ; x= 49

Answer 1

Can you find the derivative of y = x^(1/2)

Answer 2

The line will be

y - f(49) = f ' (49)*(x - 49)

Answer 3

the slope of the tangent line is the first derivative of the curve at that point

Answer 4

\[\frac{ d }{ dx }\sqrt{x} = \frac{ d }{ dx }x ^{1/2} = \frac{ 1 }{ 2 }x ^{1/2 - 1} = \frac{ 1 }{ 2 }x ^{-1/2} = \frac{ 1 }{ 2\sqrt{x} }\]

Answer 5

Just used the power rule for derivatives.

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

Answer 6

With the point x=49, y = f(49) = sqrt(49) = 7
point; (49,7)
and slope m = f '(49) = 1/(2*7) = 1/14

Form Line from Point-Slope Form

y - f(49) = f '(49) *(x-49)

Answer 7

u understand everything... @Ko-Ki

Answer 8

i think so thx

Answer 9

here is the graph

Answer 10

thanks