Question

Find ​(a) the slope of the curve at the given point​ p, and ​(b) an equation of the tangent line at p. y=−2−9x2​; ​p(2​,−38​)

Answer 1

a) -36

b) y = -36x +34

Explanation:

a) The slope is found using the derivative of the function.

f'(x) = dy/dx = 0 -9(2x) = -18x

Then at x=2, the slope is ...

f'(2) = -18·2 = -36

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b) The point-slope form of the equation can be written as ...

y = -36(x -2) -38

Simplifying to slope-intercept form, we get ...

y = -36x +34