# How do you find the equation of the line tangent to #y = (1+2x)^2#, at (1,9)?

We got:

First, we find the slope of the tangent line at

At

So, the slope of the tangent line is

Now, we use the point-slope form, which is:

where

And, we get,

A graph shows it, but it's not really clear:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the equation of the line tangent to the curve y = (1+2x)^2 at the point (1,9), we need to find the slope of the tangent line and the coordinates of the point of tangency.

First, we find the derivative of the given function y = (1+2x)^2 with respect to x.

Using the chain rule, the derivative is: dy/dx = 2(1+2x)(2) = 4(1+2x).

Next, we substitute x = 1 into the derivative to find the slope of the tangent line at x = 1: dy/dx = 4(1+2(1)) = 12.

Therefore, the slope of the tangent line is 12.

Now, we have the slope of the tangent line and the point of tangency (1,9). We can use the point-slope form of a linear equation to find the equation of the tangent line.

Using the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point of tangency, we substitute the values:

y - 9 = 12(x - 1).

Simplifying the equation, we get the equation of the tangent line:

y - 9 = 12x - 12.

Rearranging the equation, we have:

y = 12x - 3.

Therefore, the equation of the line tangent to y = (1+2x)^2 at (1,9) is y = 12x - 3.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the equation of the tangent line to curve #y=(x-1)/(x+1)#, that are parallel to the line #x-2y=2#?
- What is the equation of the tangent line of # f(x)=x^2/x+1 # at # x=2 #?
- What is the equation of the tangent line of #f(x)=(9 + x)^2 # at #x=6#?
- How do you find the equation of the tangent line to the curve #y=ln(3x-5)# at the point where x=3?
- What is the average value of the function #f(x)=cos(8x)# on the interval #[0,pi/2]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7