Question

find an equation of the line perpendicular to the tangent to the curve y=X^3 - 3x + 1 at the point (2,3)

Answer 1

What is the slope of the tangent line?

Answer 2

would it be 3?

Answer 3

No. The slope of the tangent line is the derivative of the function of the curve at that point.

Answer 4

so it would be y=3x-3

Answer 5

y' = 3x^2+3.

Answer 6

Remember power rule: the derivative of x^3 is 3x^2.

Answer 7

ohh yes! but wouldnt it be -3 not +3?

Answer 8

Ah, yes, the constant at the end is -3.
(must have had my eyes crossed when I looked at that)

Answer 9

so after i find my derivative what do i do?

Answer 10

Slope is the value of derivative at given point (2, 3)
-> f' (2) = ...

Answer 11

Sub in x.

Answer 12

so that would give me y=9?

Answer 13

y'=9, not y=9. the ' means first derivative.
But yes, that is the slope of the tangent line, so what is the slope of the line perpendicular to that?

Answer 14

1/9 or -1/9?

Answer 15

Opposite reciprocal, so -1/9.
With the slope of the line and a point on the line, you can use the point-slope formula to get your equation.

Answer 16

the point i use to find the line is (2,3)?