Step-by-step explanation:
1. -4
2. -3.25
3. 4
4. -2
5. Couldn't figure out this one
5 - 8x < 2x + 3
All x to one side, all constants to the other
2 < 10x
Simplify
0.2 < x
Use substitution
Plug in 5x for y
5x = 2x - 15
Subtract 2x
3x = -15
Divide by 3
x = -5, y = -25
Solution: (-5, -25)
1k 2k 15k
Step-by-step explanation:
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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