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If h(x) = 3x⁴ + x³ - 4x² + x - 2, find

Mathematics

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Graph of h(x) = 3x⁴ + x³ − 4x² + x − 2

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Key points of h(x) = 3x⁴ + x³ − 4x² + x − 2
Pointxy
x-intercept−1.530
Minimum−1−5
y-intercept0−2
Maximum0.14−1.93
Minimum0.61−2.24
x-intercept1.10

Step-by-step solution

2 steps

Here are the solutions to the exercises:

1. If h(x)=3x4+x3−4x2+x−2h(x) = 3x^4 + x^3 - 4x^2 + x - 2, find

i) h(0)h(0)

  1. Substitute x=0x=0 into the function h(x)h(x).

    h(0)=3(0)4+(0)3−4(0)2+(0)−2h(0) = 3(0)^4 + (0)^3 - 4(0)^2 + (0) - 2

  2. Simplify the expression.

    h(0)=0+0−0+0−2h(0) = 0 + 0 - 0 + 0 - 2 h(0)=−2h(0) = -2

    The value of h(0)h(0) is −2\boxed{-2}.

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