Write the equation of the tangent line to the graph of f at the given point / x-value
f(x)=x^2+2x+1 @ (-3,4)

Question

Write the equation of the tangent line to the graph of f at the given point / x-value
f(x)=x^2+2x+1 @ (-3,4)

anonymous · Answer

is this calculus?

anonymous · Answer

find the derivative of the function, then solve for x, x would be the slope 
then use tangent line formula and plug the points

anonymous · Answer

yes its calculus

nincompoop · Answer

got any lessons, lectures or textbooks to sort this kind of problem?

hartnn · Answer

can you find the derivative of f(x)=x^2+2x+1 first ?
f'(x) =... ?

theeric · Answer

Hi!

You have a function, which you can use to draw a curve in the $\left(x,\ f(x)\right)$ coordinate system.

Derivatives are very good for finding slope! So, you can find the slope at that point! That will help a lot with the tangent line, so then you can just use some old math to find the line.
$f(x)=mx+b$ You'll have $x$ and $f(x)$ because the problem asks about them. You'll find the slope, $m$, with the derivative. And you can solve for $b$, which is the y-intercept.

Any questions, feel free to ask!

As @hartnn suggested, you'll need to find the slope. So you find the slope equation. Then you can plug in your values to find the slope at that point. Make sure you get the equation before plugging the numbers in! You have to find the slope function and then throw in the value to get the slope.

I would find $\dfrac{df}{dx}$ to start the hard stuff. It will be a function of $x$. So then you can substitute your $x=-3$ in to find the slope.