Question

Find the coordinates of the point on y=2x^2 + 5 where the gradient is -4. Obtain the equation of the tangent to the curve at this point.

Answer given is: (-1,7) and y=-4x +3

Answer 1

To find the gradient of the curve - you need to differentiate it
\[\frac{ dy }{ dx } = 2(2x) =4x\]
the gradient will be -4 when 4x = -4 or x = -1
Subsitute x in the equation given to find y

Answer 2

You can find the tangent then with the knowledge that the tangent will pass through this point and will be of the same gradient

Answer 3

@atlas oh alright thank you so much!