How do you find the equation of a line tangent to the function #y=4/sqrtx# at (1,4)?
1 Answer
Nov 27, 2016
#y=-2x+6
Explanation:
The equation of the tangent in
#color(blue)"point-slope form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and#(x_1,y_1)" a point on the line"#
#color(orange)"Reminder"color(white)(xxx)m=dy/dx# Express
#y=4/sqrtx=4/x^(1/2)=4x^(-1/2)#
#rArrdy/dx=-2x^(-3/2)=-2/x^(3/2)#
#x=1:dy/dx=-2/1^(3/2)=-2/1=-2=m# substitute m = - 2 and
#(x_1,y_1)=(1,4)# into the equation.
#y-4=-2(x-1)rArry-4=-2x+2#
#rArry=-2x+6" is the equation of the tangent"#
