Finding Intervals of Increase/Decrease and Concavity of FunctionGiven a function f(x) on its domain, the function is increasing over parts of the domain where the function's first derivative is positive (f'(x) > 0) and is decreasi...
Given f(x) = x^4 + 4x^3 - 3. (a) Find the critical numbers; (b) Determine the intervals of increase and decrease; (c) Use the First Derivative Test to determine whether each critical point corresponds to a...
As part of exploring how functions change, we can identify intervals over which the function is changing in specific ways. We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. Similarl...
There was, however, a significant correlation between plasma drug levels and tumour response for time intervals of 1 to 48 hr. This association may imply that PDT protocols should use shorter drug-light intervals in combination with lower drug doses. This would increase safety and decrease the ...
increase, decrease, or do not affect cylindrospermopsin production. For example,Raphidiopsisproduced more cylindrospermopsin when grown on exclusively atmospheric N compared to combined N sources (Saker and Neilan2001), whereasAphanizomenongrown on atmospheric N had lower concentrations and cell ...
velocities. If this ratio equates 1, then {eq}v_1 {/eq} and {eq}v_2 {/eq} there is no change in the average velocity. If the ratio is larger than 1, then there is a decrease in the average velocity. If the ratio is smaller than 1, ...
Mesenchymal stromal cells (MSCs) hold significant potential for various applications in regenerative medicine and tissue engineering. Initially considered as a single cell type with defined characteristics, MSCs are now known as a heterogeneous cell popu
contactless techniques for Cpmeasurement have been developed, such as laser probing [6]: in a leaf sample exposed to a short laser pulse, Cpcan be derived from the energy obtained from laser heating, divided by the product of the leaf temperature increase and its physical properties (heated le...
The monotonicity and concavity of a function help us to draw the curve of the function. Answer and Explanation:1 Given It is given that {eq}f\left( x \right) = x - \sqrt x {/eq} To find the intervals where function is increasing and de...
Interval of Increasing-Decreasing Functions: To identify the intervals at which the rational functionf(x)is increasing (or decreasing), compute the derivative using the quotient rule and some basic rules of differentiation, and then put the derivativef′(x)...