Question

quite urgent, help appreciated n pellet

Let f(x) = (3x^3)/((4-5x)^5)
find the equation of the line tangent to the graph of f at x=2

Answer 1

differentiate f(x)

\[f'(x)=(4-5x)^5\times9x^2-3x^3\times5(4-5x)^4\times-5, all divided by the \square of (4-5x)^5\]

Answer 2

sub x=2 into expression for f'(x) to get the slope m of the tangent.

Then sub x=2 into f(x) to find the y-coordinate

Then line tangent equation is \[y-y_1=m(x-x_1)\]