What is the equation of the line tangent to # f(x)=x^2-(x-1)^3 # at # x=1 #?
1 Answer
May 4, 2018
Explanation:
#"to obtain the equation we require the slope m and a "#
#"point "(x_1,y_1)#
#•color(white)(x)m_(color(red)"tangent")=f'(1)#
#rArrf'(x)=2x-3(x-1)^2#
#rArrf'(1)=2-0=2#
#f(1)=1-0=1rArr(x_1,y_1)=(1,1)#
#y-1=2(x-1)#
#rArry=2x-1larrcolor(red)"equation of tangent"#
