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storchak [24]
3 years ago
15

For the function P(x) = x3 − 9x, at the point (2, −10), find the following. (a) the slope of the tangent to the curve (b) the in

stantaneous rate of change of the function
Mathematics
1 answer:
Shalnov [3]3 years ago
4 0

Answer:

3, in both a), b)

Step-by-step explanation:

a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.

Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is p'(x)=3x^2-9. In particular, the value we are looking for is p'(2)=3(2^2)-9=12-9=3.

If you would like to compute the equation of the tangent line, we can use the point-slope equation to get y=3(x-2)-10=3x-16

b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to p'(2)=3.

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