3 years ago

(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =

1 answer:

4 0

A) The slope at (1, 8) is 4.
The slope at (2, 9) is -4.
These values are computed numerically by the graphing calculator and shown in the column f'(x) in the graphic.

The derivative is y' = 10x -6x². At x=1, y' = 10-6 = 4; at x=2, y' = 20-24 = -4.

b) In point-slope form, the equations of the tangent lines are shown in the graphic.

You might be interested in

On a particular day, the wind added 5 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 5 miles

Nata [24]

now, this is pretty much the same as the one before it with Jaime, so I'll do this without much fuss.

recall d = rt.

a = Alfonso's rate

with the wind his speed is a + 5, against it is a - 5, 60 miles with it and 30 miles against it, all in the same time of t hours.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{with the wind}&60&a+5&t\\ \textit{against the wind}&30&a-4&t \end{array} \\\\\\ \begin{cases} 60=(a+5)t\implies \frac{60}{a+5}=\boxed{t}\\\\ 30=(a-4)t\\ -------------\\ 30=(a-4)\left( \boxed{\frac{60}{a+5}} \right) \end{cases} \\\\\\ 30(a+5)=(a-4)60\implies 30a+150=60a-240 \\\\\\ 390=30a\implies \cfrac{390}{30}=a\implies 13=a$