Questions: Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^3+2x^2-8x-3; a=-8, b=-1 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. By the intermediate value theorem, the function does not have at least one real zero between a and b because f(a)= and f(b)= (Simplify your answers.) B. By the intermediate value theorem, the function has at least one real zero between a and b because f(a)= and f(b)= ( Simplify your answers.) C. It is impossible to use the intermediate value theorem in this case.

Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^3+2x^2-8x-3; a=-8, b=-1 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. By the intermediate value theorem, the function does not have at least one real zero between a and b because f(a)= and f(b)= (Simplify your answers.) B. By the intermediate value theorem, the function has at least one real zero between a and b because f(a)= and f(b)= ( Simplify your answers.) C. It is impossible to use the intermediate value theorem in this case.
Transcript text: Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b . \[ f(x)=x^{3}+2 x^{2}-8 x-3 ; a=-8, b=-1 \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. By the intermediate value theorem, the function does not have at least one real zero between a and b because $\mathrm{f}(\mathrm{a})=$ $\square$ and $f(b)=$ $\square$ (Simplify your answers.) B. By the intermediate value theorem, the function has at least one real zero between a and $b$ because $f(a)=$ $\square$ and $f(b)=$ $\square$ ( Simplify your answers.) C. It is impossible to use the intermediate value theorem in this case.
failed

Solution

failed
failed

Solution Steps

Step 1: Evaluate the function at the given points

First, we evaluate the function at the points $a=-8$ and $b=-1$. We find that $f(a) = -323$ and $f(b) = 6$.

Step 2: Check the signs of $f(a)$ and $f(b)$

Since $f(a)$ and $f(b)$ have opposite signs, by the Intermediate Value Theorem, there is at least one real zero of $f(x)$ between $a$ and $b$.

Final Answer:

There is at least one real zero of the function between the given points.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the compound inequality. 3x - 2 ≤ 13 and 3x - 3 ≥ -12 Graph the solution on the number line.
failedAnswered
The life insurance policy clause that prevents an insurance company from denying payment of a death claim after a specified period of time is known as the A. Insuring clause. B. Incontestability clause. C. Misstatement of Age clause. D. Reinstatement clause.
failedAnswered
Uracil is found in most RNA, while is found in most DNA. 5-methyluracil 3-methyluracil 3-methylguanosine 5-methylguanosine
failedAnswered
Auto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean x̄ (mm) Range R (mm) 1 154.9 4.2 2 155.2 4.8 3 153.6 4.3 4 153.5 4.8 5 154.6 4.3 a) What is the value of x̄̄? x̄̄=154.36 mm (round your response to two decimal places). b) What is the value of R̄? R̄=4.48 mm (round your response to two decimal places). c) What are the UCL− and LCL− using 3-sigma? Upper Control Limit (UCL−)=155.74 mm (round your response to two decimal places). Lower Control Limit (LCLx̄)=152.98 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= square mm (round your response to two decimal places).
failedAnswered
Complete the following table. Round each of your answers to 3 significant digits. food energy content when eaten ------------ cal kcal kJ three ounces of cooked sirloin steak 2.40 × 10^5 240. 100. an ear of cooked corn 8.5 × 10^4 85.0 an ounce of breakfast corn flakes 460.