Find an equation of the tangent line to the curve at the given point ? y= (sqrt x) , (49,7)
February 20th, 2023
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: