How to find the equation of the line tangent to

Davon Trujillo

Davon Trujillo

Answered question

2022-04-22

How to find the equation of the line tangent to the graph of f at the indicated value of x? f(x)=4lnx ; x=1

Answer & Explanation

Dexter Conner

Dexter Conner

Beginner2022-04-23Added 15 answers

Explanation:
we will use the equation: yy1=m(xx1)
where (x1,y1) is a known point on the line and m = the gradient of the line at that point
to find the gradient we need to calculate f(x1)
f(x)=4lnx
y1=f(x1)=f(1)=4ln1=40=4
(x1,y1)=(1,4)
f(x)=4lnxf(x)=1x
m=f(1)=11=1
yy1=m(xx1)
y-4=-1(x-1)
y-4=-x+1
x+y=5

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