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)

a) -36

b) y = -36x +34

Step-by-step 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

positive

step-by-step explanation:

the quadrant is facing upwards