What is the equation of the line tangent to # f(x)=3/x^2# at # x=-2 #?
1 Answer
Apr 11, 2017
Explanation:
The equation of the tangent in
#color(blue)"point-slope form"# is.
#• y-y_1=m_("tangent")(x-x_1)# We require
#m_("tangent")=f'(-2)" and " (x_1,y_1)#
#f(x)=3/x^2=3x^-2#
#rArrf'(x)=-6x^-3=-6/x^3#
#rArrf'(-2)=(-6)/(-8)=3/4#
#"and "f(-2)=3/(-2)^2=3/4#
#"Using " m=3/4" and " (x_1,y_1)=(-2,3/4)#
#y-3/4=3/4(x+2)#
#rArry=3/4x+9/4larr"is equation of tangent"#
