Answer to Question #186957 in Math for rafaella

Question

a curve has the equation y=3x^2=5x+4

1- find the gradient of the curve at the point (2,6)

2- find the coordinates of the point on the curve where the gradient is -2

Answer 1

1) $f'(x)=6x-5.$

$f'(2)=12-5=7.$

2) $f'(x)=-2.$

$6x-5=-2.$

$x=\frac{1}{2}$.

$y=f(\frac{1}{2})=\frac{3}{4}-\frac{5}{2}+4=\frac{9}{4}.$

Point on the curve: $(\frac{1}{2},\frac{9}{4}).$