Step 1: Find f'(x):
f'(x) = -6x^2 + 6x
Step 2: Evaluate f'(2) to find the slope of the tangent line at x=2:
f'(2) = -6(2)^2 + 6(2) = -24 + 12 = -12
Step 3: Find f(2), so you have a point on y=f(x):
f(2) = -2·(2)^3 + 3·(2)^2 = -16 + 12 = -4
So, you have the point (2,-4) and the slope of -12.
Step 4: Find the equation of your tangent line:
Using point-slope form you'd have: y + 4 = -12 (x - 2)
That is the equation of the tangent line.
If your teacher is picky and wants slope-intercept, solve that for y to get:
y = -12 x + 20
Answer:
avn= -8 + (n-1)(-7)
Step-by-step explanation:
arithmetic sequence formula= avn= av1 + (n-1)d
av1= first number in the sequence
d= common difference
n= the number of the term to find
The common difference is -7 so d=-7 and you plug it into the equation. The first number in the sequence is -8 so av1.
There is no specific n to find so it remains n.
I hope this helps! Let me know if this helps.
12
2 multiplied by 6 is 12 and so 1 multiplied by something is 12
Hope this helps.
Answer:
a. $15.00
b. $15.00
c. they earn the same. If you divide Carl's hours by the amount of time he works, for instance, 45÷3=15, you get 15 for all of them. They earn the same.
The toy rocket hits the ground when h(t) = 0.
So, h(t) = 0 = -9t^2 + 81.
Solving the equation,
-9t^2 = -81
Dividing by -9
t^2 = 9
Taking the square root.
t = 3
The answer is 3 seconds.
