Find the slope of the tangent line to the graph off(x) = 3x2+ 5x+ 1 at thepoint (1,9).

Answer 1

The derivative of the function is f'(x)=6x+5

The value of the derivative at x=1 is f'(1)=11;

The equation tangent to the graph at the point (x0,y0) is given by y-y0=m*(x-x0) where m is slope tangent to the graph of the function.

In your case you have that the equation is y-9=11(x-1) or y=11*x-2

Best,

Davide