How do you find the equation of the tangent to

Aarav Rangel

Aarav Rangel

Answered question

2022-02-13

How do you find the equation of the tangent to the curve y=x2+2x5 that is parallel to the line y=4x-1?

Answer & Explanation

Dylan Trevino

Dylan Trevino

Beginner2022-02-14Added 7 answers

To calculate this you have to follow these steps:
1) The tangent line is parallel to y=4x+1, so it has a form of y=4x+c. (1)
2) You have to find the point where the line and the function meet. To find x you have to calculate the 1st derivative and check where it equals 4:
f'(x)=2x+2
2x+2=4
2x=2
x=1
f(1)=12+215=2
3) Now you have to calculate c for which the line (1) passes through (1,-2)
-2=4*1+c
c=-6
So finally the tangent line is: y=4x-6

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