suppose the f(x)=3x(5-4x)^3
find an equation for the tangent line to the graph of f at x=1.

I dislike these specific types of problems, so if anyone could elaborately explain how to solve these, it would be greatly appreciated.

Question

suppose the f(x)=3x(5-4x)^3
find an equation for the tangent line to the graph of f at x=1.

I dislike these specific types of problems, so if anyone could elaborately explain how to solve these, it would be greatly appreciated.

amistre64 · Answer

f' = r'l + rl'

r = 3x;  r'=3
l=(5-4x)^3;  l' = 3(5-4x)^2 (-4)

amistre64 · Answer

tangent line = f'(1)x -f'(1)1 +f(1)

amistre64 · Answer

f'(1) = 3(1)^3 + 3(1)(3)(-4)(1)^2 = 3 -36 = -33

amistre64 · Answer

tangent = -33x +33+3

y = -33x + 36  maybe?

amistre64 · Answer

do you follow it?

anonymous · Answer

yeah, it makes sense. I'm always missing one part or another, so I get half or most of the answer correct, just annoying little crap here and there that messes me up.