Question

Need this worked out please so I can understand it

a) Find the slope of the curve y= x^3 + 3 at the point P(-2, -5)

b) Find an equation of the tangent line to the curve at P(-2, -5)

Answer 1

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Answer:

a) 12

b) y +5 = 12(x +2)

Explanation:

The slope of a function is its derivative.

a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...

m = 3(-2)^2 = 12 . . . . slope at (-2, -5)

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b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)