Question

Find an equation of the tangent line to the graph of f(x)=3x^3 +2x when x=1

Answer 1

actually you need to take the derivative \(f'(x)\) then find \(f'(1)\) for the slope

Answer 2

First find the derivative of the function:
\[f' (x) = 9x^2 + 2\]
Now plug in 1 instead of x:
\[f'(x) = 9 + 2 = 11\]
So the slope is 11, now we need to find y so we plug in 1 instead of x in the original function:
\[y = 3 + 2 = 5\]
Now just plug in everything to y = mx +b and find b:
\[5 = 11 * 1 + b\]
\[ b = -6\]
So the equation is:
\[y = 11x - 6\]