How do you find the equation of the line tangent to the graph of f(x)= x(sqrt(x)-1)f(x)=x(√x−1) at the value x=4?

1 Answer
Jim G.
Aug 11, 2018

y=2x-4y=2x−4

Explanation:

"to find the equation of the tangent "y-y_1=m(x-x_1)to find the equation of the tangent y−y1=m(x−x1)

"we require m and "(x_1,y_1)we require m and (x1,y1)

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"

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