Normals to Curves (Differentiation)

[zebra1707]

Hi there
If possible can someone please review my understanding of this question.

Homework Statement

At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2

Homework Equations

The Attempt at a Solution

We are given the gradient of the normal as -1/2
Therefore gradient of the tangent = 2

dy/dx = 4x - 7 = 2
4x = 9
x = 2.25 (2 1/4)

plug into y = 2(2.25)^2 - 7(2.25) - 15
y = -20 5/8

Therefore the point on the parabola - where a normal to the parabola will have a gradient of
-1/2 = (2 1/4, -20 5/8).

 

[tiny-tim]

Hi zebra1707!

(try using the X² tag just above the Reply box )

At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2
…
We are given the gradient of the normal as -1/2
Therefore gradient of the tangent = 2
…
Therefore the point on the parabola - where a normal to the parabola will have a gradient of
-1/2 = (2 1/4, -20 5/8).

Looks good!