What is the equation of the line with

George Michael

George Michael

Answered question

2022-04-10

What is the equation of the line with slope 3 which is tangent to the curve f(x)=7xx2?

Answer & Explanation

Zaria Lamb

Zaria Lamb

Beginner2022-04-11Added 8 answers

If f(x)=7xx2
then the slope (for any general x value) is f'(x)=7-2x
when the slope is m=f'(x)=3
then 7-2x=3
-2x=-4
x=2
If x=2 then
f(2)=7(2)22=144=10
and the point on the curve were f'(x)=3 occurs at (2, 10)
Therefore, for the tangent, we have a slope of m=3 and a point (2, 10)
Using the slope-point form of the equation:
y-10=3(x-2)
or
y=3x+4

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