ACT Math : How to find the equation of a tangent line

Example Questions

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Example Question #11 : How To Find The Equation Of A Tangent Line

What is the equation of a tangent line to

at the point

?

Explanation:

To find an equation tangent to

we need to find the first derviative of this equation with respect to  to get the slope  of the tangent line.

So,

due to power rule .

First we need to find our slope by plugging our  into the derivative equation and solving.

Thus, the slope is

.

To find the equation of a tangent line of a given point  we plug our point into

.

Therefore our equation is

Once we rearrange, the equation is

Example Question #12 : How To Find The Equation Of A Tangent Line

What is the equation of a tangent line to

at the point

?

Explanation:

To find an equation tangent to

we need to find the first derviative of this equation with respect to  to get the slope  of the tangent line.

So,

due to power rule .

First we need to find our slope by plugging our  into the derivative equation and solving.

Thus, the slope is

.

To find the equation of a tangent line of a given point  we plug our point into

.

Therefore our equation is

Once we rearrange, the equation is

Example Question #13 : How To Find The Equation Of A Tangent Line

What is the equation of a tangent line to

at the point

?

Explanation:

To find an equation tangent to

we need to find the first derviative of this equation with respect to  to get the slope  of the tangent line.

So,

due to power rule .

First we need to find the slope by plugging our  into the derivative equation and solving.

Thus, the slope is

.

To find the equation of a tangent line of a given point  we plug our point into

.

Therefore our equation is

Once we rearrange, the equation is

Example Question #14 : How To Find The Equation Of A Tangent Line

What is the equation of a tangent line to

at the point

?

Explanation:

To find an equation tangent to

we need to find the first derviative of this equation with respect to  to get the slope  of the tangent line.

So,

due to power rule .

First we need to find the slope by plugging our  into the derivative equation and solving.

Thus, the slope is

.

To find the equation of a tangent line of a given point  we plug our point into

.

Therefore our equation is

Once we rearrange, the equation is

Example Question #15 : How To Find The Equation Of A Tangent Line

What is the equation of a tagent line to

at the point

?

Explanation:

To find an equation tangent to

we need to find the first derviative of this equation with respect to  to get the slope  of the tangent line.

So,

due to power rule .

First we need to find the slope by plugging our  into the derivative equation and solving.

Thus, the slope is

.

To find the equation of a tangent line of a given point  we plug our point into

.

Therefore our equation is

Once we rearrange, the equation is

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