Question

What is the equation of the tangent line of `f(x) =x^5-3x^4+x^2/2` at `x=2`?

Answer 1

`y=-14x+14`

Explanation:

First of all, we need to find the coordinates of `f(x)` @ `x=2`. `f(2)=`(and I'm not showing all the work, you're in calc)`32-48+2=-14`.

Now we know the point `(2, -14)`

Next, to find the slope, take the derivative, which according to the power law would be `f'(x)=5x^4-12x^3+x`. `f'(2)` is the slope at 2 and results in a value of `-14` (coincidence? I think not).

So we know our equation is in the form `y=mx+b` and we have determined that `m` is `-14`. We know the point `(2, -14)` on the graph of f(x).

Solve for `b`:
`-14=-14(2)+b`
`-14=-28+b`
`14=b`

So the equation of tangent line is `y=-14x+14`.