Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1.
a) f(x) = x
b) f(x) = x^4
a) df(x) dx = 1 so slope = 1
since f(0) = 0, passes through origin and (1,1)
that is y = x
b) slope = 4 x^3
at x = 1, y = 1
and m = 4
1 = 4(1) + b
b = -3
so
y = 4x - 3