Question

PLEASE HELP Find the area of the region bounded by the curve y = f(x) = x^3 – 4x + 1 and the tangent line to the curve y = f(x) at (–1,4).

Answer 1

First find the slope of the tangent line, then use the point slope formula to find the equation of the line

y=-x+3

Now, find out where this crosses your original function. That will give you your limits of integration. Then, you will integrate A(x)-B(x), where A is your higher function and B is your lower function--that is, A(x) is -x+3 and B(x)=f(x)=x^3-4x+1

See how far you get with that--tell me if you get stuck.