What is the equation of the line tangent

Ekwadorkadba3

Ekwadorkadba3

Answered question

2022-04-09

What is the equation of the line tangent to f(x)=3x2+e1x at x=1?

Answer & Explanation

Cesar Mcfarland

Cesar Mcfarland

Beginner2022-04-10Added 8 answers

Step 1: Differentiate the function
f(x)=ddx(3x2)+ddx(e1x)
=6xe1x
Step 2: Find the slope of tangent line at x=1
m=f(1)=6(1)e11=5
Step 3: Find y coordinate of the function when x=1
f(1)=3(1)2+e11=3+1=4
So, original point of the graph is (1,4)
To find equation of the line we can us point slope formula
yy1=m(xx1), when x1 & y1 is the point on original equation
m=5 (1,4)
y-4=5(x-1)
y=5x5+4
y=5x1

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