test review questions

Question

Answer 1

4)

f(x) = 2x⁴ - 8x³+8x²+20

Take derivative both sides with respect to x.

f'(x) = (2x⁴ - 8x³+8x²+20)'

       = 8x³ - 24x² + 16x

For horizontal tangent slope = 0

f'(x) =0

8x³ - 24x² + 16x =0

8x (x² - 3x + 2) =0

x =0

x² - 3x + 2 = 0

x² - 2x - x + 2 = 0

x (x -2) -1 (x - 2) = 0

(x -1) (x -2)= 0

x = 1, 2

At x = 0

y = 2(0)⁴ - 8(0)³+8(0)²+20 =20

At x = 1

y = 2(1)⁴ - 8(1)³+8(1)²+20 =22

At x = 2

y = 2(2)⁴ - 8(2)³+8(2)²+20 =20

So points are (0, 20),(1, 22), and (2,20)

Answer 2

5)

Apply quotient rule in derivatives

 

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