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

Question

anonymous · Answer

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

anonymous · Answer

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:
$$y = 11x - 6$$