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Chapter 4: Q. 10 (page 247)

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

Short Answer

Expert verified

The function has a zero between 0 and 4.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=-2x2-3x+8

02

Step 2. Explanation

Evaluate the function at 0 and 4.

f(0)=-2(0)2-3(0)+8=0-0+8=8andf(4)=-2(4)2-3(4)+8=-32-12+8=-36

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

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