Calculus Answers

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x1/4 - 12x

3.f(x)= ____ $\sqrt[4]{x}$ $\sqrt[4]{x^3} - \underset{x^6} + \frac{2}{3} x^6$

4.f (x) = $\underset{x^-6}{=} -$ ____ x² + $\sqrt[4]{x}$

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = sin(x),    0 ≤ x < 𝜋

2

A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function S(t) = At^pe^−kt

 (where t > 0) is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.03, p = 4, k = 0.05, and t is measured in minutes, estimate the times t corresponding to the inflection points. (Round your answers to two decimal places.)t = min (smaller value) t = min (larger value)

Raggs Limited, a clothing firm, determines that the revenue, in rand, of selling x dresses is given by the function R(x) = x(450 − 0,050x). It also determines that the total cost, in rand, of producing x dresses is given by the function C(x) = 40 000 + 0,025x2. The marginal profit when x dresses are produced and sold, is given by the function

(i)Find the volume of the solid that is generated by revolving the region bound by the

graphs of 𝑦 = 𝑥2 and 𝑦2 = 𝑥 about the 𝑦 − 𝑎𝑥𝑖𝑠.

Find the asymptotes of the curve 𝑥2𝑦 − 𝑥𝑦2 + 𝑥𝑦 + 𝑦2 + 𝑥 − 𝑦 = 0.

Write the word continuous if the given function is continuous on each of the given intervals otherwise write the word not continuous f(x)=x+5/x^-9 a.(0,9] b.(-3,3)

Prove that x(1 + x) > (1 + x) In(1 + x) > x