What is the equation of the tangent line

Salvatore Dorsey

Salvatore Dorsey

Answered question

2022-03-16

What is the equation of the tangent line of f(x)=x3+2x23x+2 at x=1?

Answer & Explanation

Setartetaliffvz5

Setartetaliffvz5

Beginner2022-03-17Added 3 answers

Explanation:
To find the equation of the tangent in the form y=mx +c , where m represents the gradient and c , the y-intercept.
Require to find m and c . m can be found by evaluating f'(1) and c by evaluating f(1).
f(x)=3x2+4x3
and f(1)=3(1)2+4(1)3=4=m gradient of tangent
partial equation is: y=4x+c
now f(1)=(1)3+2(1)23(1)+2=2(1,2) is tangent point
substitute (1,2) into y = 4x + c to calculate value of c.
hence : 2=4+cc=2
equation of tangent is y=4x-2

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