Question

Please help: find an equation of the tangent line to the graph of f at P.
f(x)= 4x^1/4 *the exponent is 1/4*
P(81,12)

Answer 1

Find the slope of the tangent at x = 81.
To do that, find f'(x) which is the derivative of f(x).
Then evaluate f'(x) when x = 81. That will be the slope m of the tangent line.
Plug it into the equation y = mx + b
We still need to find b.
Since the tangent passes through the point (81, 12), put x = 81 and y = 12 in the y = mx + b equation and solve for b.