1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values?

2. What are inflection points? How do you find them?

Expert Solution

milcah answered 2 years ago

1. What is a critical number of a function f ? What is the connection between...

1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values? 2. What are inflection points? How do you find them? 3. What does the sign of the derivative, f ', tell us about the function? What does the sign of the 2nd derivative, f ", tell us about the function? 4. What does it mean to say that a function is concave upward? Concave downward? 5. What does...

(a) Find the critical numbers of the function f(x) = x8(x − 1)7. (b) What does...

(a) Find the critical numbers of the function f(x) = x8(x − 1)7. (b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers? (c) What does the First Derivative Test tell you? (Enter your answers from smallest to largest x value.)

1. Find the critical numbers of the function f (x) = x^3− 12x in the interval...

1. Find the critical numbers of the function f (x) = x^3− 12x in the interval [0, 3]. Then find the absolute maximum and the absolute minimum of f(x) on the interval [0,3]. 2. Using only the limit definition of derivative, find the derivative of f(x) = x^2− 6x (do not use the formulas of derivatives).

Find the extreme values of f on the region described by the inequality. f(x, y) =...

Find the extreme values of f on the region described by the inequality. f(x, y) = e−xy; x2 + 4y2 ≤ 1

Determine the location and value of the absolute extreme values of: f(x) = sin (1 /x...

Determine the location and value of the absolute extreme values of: f(x) = sin (1 /x ) on [ 1/5 , 2].

1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θ

1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θ θ=? 2) Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x/(x^2 − x + 9), [0, 9] 3) f(x) = 3x3 + 4x2 + 7x + 5, a = 5 (f −1)'(a) = ?

Find the two critical values of the function f (x) = x2/5 (5 − 2x).

Explain what an extreme value is. Include in your answer (1) the effect extreme values have...

Explain what an extreme value is. Include in your answer (1) the effect extreme values have on the median, if any, and (2) the effect extreme values have on the mean, if any.

Consider a function that describes the values of Cp as a function of temperature, relative to...

Consider a function that describes the values of Cp as a function of temperature, relative to the water vapor (gas), in the temperature range between 100 oC and 700 oC: Cp(H2 O, g) (J K-1mol-1) = 30.54 + 0.01029T (T / K) (a) Calculate the amount of heat required to raise the temperature of two moles of water vapor at constant pressure to 100 oC to 500 oC. b) Calculate the entropy variation associated with the heating process referred to...

Consider the function ?(?)=(?^(4/5))*(?−3). This function has two critical numbers ?<? 1) Then ?= ? and...

Consider the function ?(?)=(?^(4/5))*(?−3). This function has two critical numbers ?<? 1) Then ?= ? and ? = ?. 2) For each of the following intervals, tell whether ?(?) is increasing or decreasing. (−∞,?]: ? [?,?]: ? [?,∞): ? 3) The critical number A is ? and the critical number B is ? (a relative maximum / a relative minimum / neither max nor min ) There are two numbers ?<? where either ?″(?)=0 or f″(x) is undefined. 4) Then C...

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