Chapter 4: Q. 10 (page 247)

Use the Intermediate Value Theorem to show that the function $f (x) = - 2 x^{2} - 3 x + 8$ has at least one real zero on the interval $[0, 4]$

Short Answer

Expert verified

The function has a zero between 0 and 4.

Step by step solution

Step 1. Given Information

The given function is $f (x) = - 2 x^{2} - 3 x + 8$

Step 2. Explanation

Evaluate the function at 0 and 4.

$f (0) = - 2 {(0)}^{2} - 3 (0) + 8 = 0 - 0 + 8 = 8 a n d f (4) = - 2 {(4)}^{2} - 3 (4) + 8 = - 32 - 12 + 8 = - 36$

Thus, we have $f (0) > 0 a n d f (4) < 0$ and by intermediate value theorem, function has a zero between 0 and 4.

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Use the Intermediate Value Theorem to show that the function $f (x) = - 2 x^{2} - 3 x + 8$ has at least one real zero on the interval $[0, 4]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Use the Intermediate Value Theorem to show that the function f(x)=-2x2-3x+8has at least one real zero on the interval0,4

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Step by step solution

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Use the Intermediate Value Theorem to show that the function $f (x) = - 2 x^{2} - 3 x + 8$ has at least one real zero on the interval $[0, 4]$