For y fx x4 9x3 8 find dy and delta y given x 5 and del

For y = f(x) = x^4 - 9x^3 + 8, find dy and delta y, given x = 5 and delta x = -0.2. dy =

Solution

f(x) = x⁴ - 9x³ +8 , x = 5 , x = -0.2

dy/dx = 4x^4-1 - 9(3)x^3-1 + 0

==> dy/dx = 4x³ - 27x²

==> dy/dx @ x = 5 = 4(5)³ - 27(5)² = -175

dy/dx = -175

==> dy = -175 dx

==> dy = -175 (-0.2)

==> dy = 35

f(5) = 5⁴ - 9(5)³ +8 = -492

f(5 - 0.2) = f(4.8) = 4.8⁴ - 9(4.8)³ +8 = -456.4864

y = f(x + x) - f(x) = f(4.8) - f(5)

==> -456.4864 - (-492)

==> -456.4864 + 492

==> 35.5136

Hence dy = 35 and y = 35.5136