MHB How Do You Find the Equation of a Tangent Line at a Given Point?

[cgr4]

The line y = ax + b is tangent to y=x³ at the point P = (-3,-27). Find a and b.

I'm pretty lost on this one.

Here's my initial thoughts. Find (a) first.

(a) is equal to the slope which is the derivative of x³

So (a) would be equal to 3(-3)² ?

Not quite sure where to start on this one.

 

[Evgeny.Makarov]

The line y = ax + b is tangent to y=x³ at the point P = (-3,-27). Find a and b.

(a) is equal to the slope which is the derivative of x³

So (a) would be equal to 3(-3)² ?

Yes. Once you know $a$, $y=-27$ and $x=-3$, it is easy to find $b$.

 

[cgr4]

Yes. Once you know $a$, $y=-27$ and $x=-3$, it is easy to find $b$.

so a = 27

so, y = 27(-3) + b

-27 = -81 + b

therefore b = 64?

 

[Evgeny.Makarov]

-27 = -81 + b

therefore b = 64?

Correct, except that 81 - 27 = 54.