Question

the equation of a tangent to the curve of f(x)=ax3 + bx is y-x-4=0 if the point of contact is (-1;3). calculate a and b

Answer 1

im not sure i just want to know how to get to the answer what are the steps

Answer 2

first find first derivative of f(x) i.e f'(x)=3ax^2 +b
and since the tangent is at (-1,3) therfore the f'(x)=3a+b at(-1,3)
now slope of the tangent line is 1 thus 3a+b=1
further the curve passes through (-1,3)
then 3=-a-b
thus solving the two eq. as obtained
we have a=2 and b=-5

Answer 3

the slope of the tangent to a curve is given by f'(x)

Answer 4

sorry can you please explain how you got to the 2 equations