Question

The gradient of the curve


`y = {3x}^(x2) + 11x + 7`
at point p(x,y) is -1. Find the coirdinate of P.​

Answer 1

Coordinate of P is (-2, -3)

Explanation:

Gradient is the derivative of the curve:

`y = {3x}^(2) + 11x + 7 \\ \\ (dy)/(dx) = 6x + 11`

but dy/dx is -1 :

`6x + 11 = - 1 \\ 6x = - 12 \\ x = - 2`

substitute for x :

`y = 3( - 2) {}^(2) + 11( - 2) + 7 \\ y = - 3`