Question

Find the equation of the tangent line to the curve y = x^3 − 2x + 3 when x = −1. (Show clear steps).

Answer 1

Answer:

y=x+5

Step-by-step explanation:

Plug in -1 for x to find the tangent point:

y = (-1)^3 - 2(-1) + 3 = 4

y = 4

So, the tangent point is (-1,4)

Then find the slope:

take the derivative of y = x^3 - 2x + 3

3x^(3-1) - 2x^(1-1) + 0 (power rule)

dy/dx = 3x^2 - 2

then plug in x= -1 to find the slope...

m = 3(-1)^2-2 = 1

m=1

now we find the line with the slope m=1 passing through the points (-1,4)

using the equation of a line: (y-y₁) = m*(x-x₁)

So,

(y-4) = 1(x+1)

[Answer] y = x+5

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