Denise and Jacqueline are training for a swimming and running race.
1 answer:
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Answer:
A) -9/2
B) 9/4
C) -9/2, same as A)
Step-by-step explanation:
We are given that . We use the properties of integrals to write the new integrals in terms of I.
A) . We have used that ∫cf dx=c∫f dx.
B) . Here we used that reversing the limits of integration changes the sign of the integral.
C) It's the same integral in A)
Answer:
look below
Step-by-step explanation:
y = 2 (x + 3)^2 - 2
Geometric figure: parabola
Alternate forms:
y = 2 (x + 2) (x + 4)
y = 2 (x^2 + 6 x + 8)
-2 x^2 - 12 x + y - 16 = 0
Expanded form:
y = 2 x^2 + 12 x + 16
Roots:
x = -4
x = -2
<u>Properties as a real function: </u>
Domain - R (all real numbers)
Range - {y element R : y>=-2}
Partial derivatives:
d/dx(2 (x + 3)^2 - 2) = 4 (x + 3)
d/dy(2 (x + 3)^2 - 2) = 0
Implicit derivatives:
(dx(y))/(dy) = 1/(12 + 4 x)
(dy(x))/(dx) = 4 (3 + x)
Global minimum:
min{2 (x + 3)^2 - 2} = -2 at x = -3
