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

1 Answer
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#.