Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Answer:
Answer:
t ≅ 5.09 min
Step-by-step explanation:
we have that if in 4000 L/sol there is 132 kg salt and the pumping speed is 12L/s, we must find how much of salt is pumping per second and then find the amount of salt remaining
12L/s*132kg salt/4000L = 0.396 Kg salt/s, this means that 0.396 kg per second comes out , It should be found that the amount of salt must be drained so that only 11 kg of salt remain
132kg salt - 11 kg salt = 121 kg salt, so
121Kg salt*s/0.396Kg salt ≅ 305.55 s ⇒ 305.55s*min/60s ≅ 5.09 min
Step-by-step explanation:
Answer:
440 miles
Step-by-step explanation:
miles ÷ gallons
132 ÷ 6 = 22
22 miles per gallon
22 × 20 = 440