What is the equation of the line tangent

Alessandra Carrillo

Alessandra Carrillo

Answered question

2022-04-10

What is the equation of the line tangent to f(x)=x2x at x=2?

Answer & Explanation

Egerlandsq0z

Egerlandsq0z

Beginner2022-04-11Added 14 answers

Explanation:
From the given, f(x)=x2x at x=2
compute for the point (x1,y1)
x1=2
y1=f(x1)=f(2)=222=2
therefore (x1,y2)=(2,2)
find the first derivative then use x=2 to find the slope m
f'(x)=2x-1
slope m = f'(2)=2*2-1=3
m=3
For the tangent line:
Use yy1=m(xx1)
y-2=3*(x-2)
y=3x-6+2
y=3x-4 the equation of the tangent line.

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