How do you show the line y=6x-5 is a tangent

Zouridt6

Zouridt6

Answered question

2022-02-11

How do you show the line y=6x-5 is a tangent to the quadratic equation f(x)=5x214x+15?

Answer & Explanation

Sam Jensen

Sam Jensen

Beginner2022-02-12Added 13 answers

Show the line y=6x-5 is a tangent to the quadratic equation
f(x)=5x214x+15
For f(x)=5x214x+15, the slope of the tangent is given by :
f'(x)=10x-14
The slope of y=6x-5 is 6. (x=2)
Find the value of x at which the slope of the tangent is 6.
Find the corresponding y value on the graph of f(x)=5x214x+15.
(y=5(22)14(2)+15)
Finally, finish finding the equation of the tangent line at that point to see that it is, indeed y=6x-5.

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