Question

Find the equation for the tangent line of f(x)=−3x2−7x+3 at x=3.

Answer 1

Hello : 
the equation for the tangent line at point : A(x' , y' ) is :
y - y' = f'(x') (x-x')........f'(x') the slope
in this exercice : 
f(x) = -3x²-7x+3  and : x' = 3
y' = f(3) = -3(3)²-7(3) +3 =- 45
but : f'(x) = -6x-7   ...( derivate of : f(x) )
f'(3) = -6(3) -7 = - 25

the equation for the tangent line is : y - (-45) = -25(x-3)
y = -25x+30