Question

Find the point(s) on the curve y = x ^ 3 + 7x at which the normal line has the equation y = x + 20​

Answer 1

Answer:

the curve is y = x ^ 3 + 7x.

the normal of the line is y = x +20.

We know that that normal line cut the curve at an point .

so, putting the value of y in the curve's equation we get,x ^ 3 + 7x=x +20

or,x ^ 3 + 6x -20=0

or,(x-2)(x^2+2x+10)=0

now,

(x-2)=0

or,x=2

&root of this equation (x^2+2x+10)=0 are imaginary.

now putting x=2 in the equation of the curve we get,y = 2^3+7*2=8+14=22

one point on the curve is (2,22)

Answer 2

Step-by-step explanation:

the curve is y=x^3 + 7x.

the normal of the line is y = x +20.

We know that that normal line cut the curve at an point.

so, putting the value of y in the curve's equation we get,x^3 + 7x=x +20

+ 6x -20=0 or,(x-2)(x^2+2x+10)=0

now,

(x-2)=0

or,x=2

&root of this equation (x^2+2x+10)=0 are imaginary.

now putting x=2 in the equation of the curve we get,y = 2^3+7*2=8+14=22

one point on the curve is (2,22)