Answer:
Step-by-step explanation:
Domain is the x values. The interval of x-values that the function encompasses are from 0 inclusive to 7 exclusive. In interval notation that is [0, 7). The range is the y values. The interval of y-values that the function encompasses are from what looks like -2 to 4. In interval notation that is [-2, 4]. The domain goes from the lowest x-value to the highest; the range goes from the lowest y-value to the highest.
9514 1404 393
Answer:
a) 12
b) y +5 = 12(x +2)
Step-by-step 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)
Answer:
p (6, -4)-------------->p'(6,4)