10. For what values of x in the interval [1, 4] does the graph of f(x)=−x^3+6x^2...

10. For what values of x in the interval [1, 4] does the graph of f(x)=−x^3+6x^2 −9x−1 satisfy Rolle’s Theorem? Include a sketch and a brief explanation of what’s going on in this problem.

11. Evaluate each limit. Provide a brief explanation of how you can apply the “top heavy, bottom heavy, it’s a tie” strategy.

lim x→∞ 1 / (2x+sinx)

12) Draw a diagram and solve: What is the exact area of the biggest isosceles triangle you can inscribe above the x-axis and under the parabola y=4−x2? Hint: the vertex of the riangle is at the origin an the base of the triangle is parallel to the x-axis

Expert Solution

milcah answered 2 years ago

1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2...

1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2 + 9x + 1 in the following intervals: a) [0,5] b) [-1,2] 2. A company produces and sells x number of calculators per week. The functions for demand and cost are the following: p = 500 - 0.5x and c(x) = 10,000 + 135x. Determine: a) Function of weekly revenue b) Price and number of calculators that have to be sold to maximize revenue...

Find all values of x on the interval -4< x< 3 for which the graph of...

Find all values of x on the interval -4< x< 3 for which the graph of g has a point of inflection. Give a reason for your answer.

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x)...

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps: i. Compute f 0 (x) and f 00(x). ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2. iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x)...

1) Find the exact absolute max and exact min for f(x)=x^3-3x^2-6x+4 on the closed interval [0,3]...

1) Find the exact absolute max and exact min for f(x)=x^3-3x^2-6x+4 on the closed interval [0,3] 2) Let f be continuously differentiable function on the Reals with the following characteristics: - f(x) is increasing from intervals (0,2) and (4,5) and decreasing everywhere else - f(x) > -1 on the interval (1,3) and f(x) < -1 everywhere else Suppose g(x) = 2f(x) + (f(x))^2. On which interval(s) is g(x) increasing?

Suppose f(x)= 2x^3- 6x^2 + 1 For what x is f(x) increasing? decreasing? What are the...

Suppose f(x)= 2x^3- 6x^2 + 1 For what x is f(x) increasing? decreasing? What are the local minimum and maximum values of the function f (if any)?

The absolute maximum values of f(x)=x^3-3x^2+12 on the closed interval [−2, 4] occurs at x =

On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x)...

On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

f(x)= x^3+9x^2-6x+1997 a)find the taylor series for f(x) centered at x=1 b) using desmos, graph you...

f(x)= x^3+9x^2-6x+1997 a)find the taylor series for f(x) centered at x=1 b) using desmos, graph you taylor series for f(x) centered at x=1

f(x)= 1/3x^3 + 5/2x^2 - 6x + 4; [-9,3] The absolute maximum value is ____ at...

f(x)= 1/3x^3 + 5/2x^2 - 6x + 4; [-9,3] The absolute maximum value is ____ at x = ___ (Use comma to separate answers as needed. Round to two decimal places as needed) The absolute minimum value is ____ at x = ___ (Use comma to separate answers as needed. Round to two decimal places as needed)

Find f. f ''(x) = 4 + 6x + 24x2, f(0) = 4, f (1) = 12

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