Explanation Definition used: Increasing function: Let f be a function with its derivative defined on some interval. Then the function is said to be increasing if the inequality f ( x ) > 0 holds for every x in the interval. Decreasing function: Let f be a function with its derivative defined on some interval. Then the function is said to be decreasing if the inequality f ( x ) < 0 holds for every x in the interval. Calculation: The given function is, f ( x ) = a x 2 + b x + c , where a > 0 . Obtain the derivative of the function f ( x ) = a x 2 + b x + c as follows. f ′ ( x ) = a ( 2 x ) + b ( 1 ) + 0 = 2 a x + b Assume that there exists a critical number x ′ such that it satisfies the conditions f ′ ( x ′ ) = 0 or f ′ ( x ′ ) does not exist. Equate f ′ ( x ′ ) = 0 and obtain the value of x ′ . f ′ ( x ′ ) = 0 2 a x ′ + b = 0 2 a x ′ = − b x ′ = − b 2 a That is, the critical number is − b 2 a . Therefore, the critical points are x ′ = − b 2 a . These points determine the interval ( − ∞ , − b 2 a ) , ( − b 2 a , ∞ ) . Consider a point from each interval and find the corresponding value of the derivative function. Consider a point x = − b 2 a − 1 2 a on the interval ( − ∞ , − b 2 a ) and find the sign of the derivative function as follows. f ′ ( − b 2 a − 1 2 a ) = 2 a ( − b 2 a − 1 2 a ) + b = − b − 1 + b = − 1 < 0 Consider a point x = − b 2 a + 1 2 a on the interval ( − b 2 a , ∞ ) and find the sign of the derivative function as follows

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Author: RITCHEY

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Chapter 13.1, Problem 38E

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To find: The vertex and intervals where f(x)=ax2+bx+c increases and decreases, and also verify it with the result found in chapter 10.

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Chapter 13.1, Problem 37E

Chapter 13.1, Problem 39E

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4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of about

6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4

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Chapter 13 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

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The vertex and intervals where f ( x ) = a x 2 + b x + c increases and decreases, and also verify it with the result found in chapter 10.

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To find: The vertex and intervals where f(x)=ax2+bx+c increases and decreases, and also verify it with the result found in chapter 10.

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Chapter 13 Solutions