HELP! Differentiation maths homework?

Question

The normal at the point P to the curve y=2-x^3 has gradient 3. What is the x - coordinate of P?
A) 1
B) 1/3
C) -1/3 or 1/3
D) -1 or 1

 

Answer 1

The Curve Equation is y = 2 - x³.

Gadient or slope m = 3

To find the slope, We differentiate the curve Equation with respect to x.

y = 2 - x³

y' = -3x²

y' = -3x²

Normal slope m1*m2 = -1

m* (-3x²) = -1

m = 1/3x²

Now we know that m =3

3 = 1/3x²

x² = 1/9

x = ±1/3

Therefore slope of the Curve normal to the point is -1/3 and 1/3.

Option (c) is correct.