Question

find the co-ordinates of the point at which the tangent to the curve y=3x^2 + 5x -7 is perpendicular to the line 2y + x -5=0

Answer 1

well the gradient m1 if you rearrange 2y + x - 5 is -1/2
so m2 = 2

I am confused as what to do next.

Answer 2

No, find the derivative of the curve, and solve for when \(f'(x)=-\frac{1}{2}\). Then, find which of the two points in which that is the case is also a point on the line given.

Answer 3

ok, now i know waht to do
yes you are right
since you found the slope of the line, you need to find the perpendicular slope

which is m=2

now you find the derivative of the parabola

and determine when f'(x)=2

once you find x
plug that back into the parabola to find your y coordinate

enjoy

Answer 4

Yes, sorry, I forgot to check if the first post was right on the slope. The perpendicular does have a slope of 2.