Question

Find the equation of the line tangent to the graph of f at (3, 140), where f is given by f(x) = 8x^3 − 9x^2 + 5.

Answer 1

First of all, take the derivative of function f(x), you get:\[f'(x)=24x ^{2}-18x\]
Then, the tangent line has equation of the form:
\[y=f(x_{0})+f'(x _{0})*(x-x _{0})\]
The tangent line goes through (3,140), thus you get \[f(x _{0})=f(3)=140\] already.
Then, calculate \[f'(x _{0})\] and finally, you get the equation of the tangent line.

Answer 2

thanks