Bissoy.com
Doctors Medicines MCQs Q&A

What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which increases with x?

What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which increases with x? Correct Answer x > 4 or x < -1

Since f(x) = 2x3 – 9x2 – 24x + 5 Therefore, f’(x) = 6x2 – 18x + 24 = 6(x – 4)(x + 1) If x > 4, then, x – 4 > 0 and x + 1 > 0 Thus, (x – 4)(x + 1) > 0 i.e., f’(x) > 0, when x > 4 Again, if x < -1, then, x – 4 < 0 and x + 1 < 0 So, from here, (x – 4)(x + 1) > 0 i.e., f’(x) > 0, when x < -1 Hence, f’(x) > 0, when x > 4 Or x < -1 Therefore, f(x) increases with x when, x > 4 or x < -1

Related Questions

What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which decreases with x?
9x2 - 24x এর সাথে কত যোগ করলে যোগফল পূর্ণ বর্ণ হবে?
Engines are rated at specified conditions. Then which of the following statements are correct? 1. Power developed increases as local temperature increases. 2. Power developed increases as local temperature decreases 3. Power developed is not dependent on local temperature. 4. Power developed increases as local atmospheric pressure increases. 5. Power developed increases as local atmospheric pressure decreases.
Find the remainder when 2x3- 9x2 + x + 12 is divided by x - 1.
Which among the following statements about Satpura Range is/are correct? 1. Mountain Range Satpura and Vindhya Found in the Eastern part of India. 2. The range, the name of which means “Seven Folds,” forms the watershed between the Narmada (north) and Tapti (south) rivers. 3. If peaks more than 4,000 feet (1,200 meters) high, the Satpura Range includes the Mahadeo Hills to the north, the Maikala Range to the east, and the Rajpipla Hills to the west.
The digitization process i.e. the digital image has M rows and N columns, requires decisions about values for M, N, and for the number, L, of max gray levels is an integer power of 2 i.e. L = 2k, allowed for each pixel. If we assume that the discrete levels are equally spaced and that they are integers then they are in the interval __________ and Sometimes the range of values spanned by the gray scale is called the ________ of an image. and static range respectively b) and dynamic range respectively c) and static range respectively d) and dynamic range respectively
Validate the statement: “For a given image in one-dimension given by function f(x, y), to sample the function we take equally spaced samples, superimposed on the function, along a horizontal line. However, the sample values still span (vertically) a continuous range of gray-level values. So, to convert the given function into a digital function, the gray-level values must be divided into various discrete levels.”
What will be the maxima for the function f(x) = x4 –8x3 + 22x2 –24x + 8?
What will be the minima for the function f(x) = x4 – 8x3 + 22x2 – 24x + 8?
Workability of concrete can be measured using slump, compaction factor and Vee-bee time. Consider the following statements for workability of concrete: (i) As the slump increases, the Vee-bee time increases. (ii) As the slump increases, the compaction factor increases. Which of the following is TRUE?