How do you find the equation of the line tangent to the graph of #f(x)= x(sqrt(x)-1)# at the value x=4?
1 Answer
Aug 11, 2018
Explanation:
#"to find the equation of the tangent "y-y_1=m(x-x_1)#
#"we require m and "(x_1,y_1)#
#m=f'(4)" and "y_1=f(4)#
#f(4)=4(2-1)=4rArr(x_1,y_1)=(4,4)#
#f(x)=x(x^(1/2)-1)=x^(3/2)-x#
#f'(x)=3/2x^(1/2)-1#
#f'(4)=3/2 .2-1=2#
#y-4=2(x-4)#
#y=2x-4larrcolor(red)"is equation of tangent"#
