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
Open up the brackets
Collect like terms
Simplify
Therefore, your answer is 12.
Fine increase = 78 - 65 = 13
Increase rate = 13/65 x 100% = 20%
Discounted amount = 560 - 476 = 84
Discount rate = 84 / 560 x 100% = 15%
Answer 2 is 12
Step-by-step explanation:
more than 11 is 12
