Find an equation of the tangent line to the curve at the given point ? y= (sqrt x) , (49,7)

1 Answer
Gió
Mar 17, 2015

First we can find the slope of your tangent calculating the derivative of your function and substituting the value #x=49# in it:
1) #f(x)=sqrt(x)#
#f'(x)=1/(2sqrt(x))#
2) for #x=49# you get:
#f'(49)=1/(2sqrt(49))=1/14#
3) the equation of the tangent with slope #m=1/14# and passing through (#x_0=49, y_0=7#) can be written as:
#y-y_0=m(x-x_0)#
#y-7=1/14(x-49)#
#y=x/14+7/2#

Graphically:
enter image source here

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