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

1 Answer
evant939012
Apr 26, 2018

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.

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