Math 3 (9.10)
Math 3 Notes (September 2010)
Find the derivative of the following function: h(x) = (3x^4 + 2x^3 + 5) (x^2 - 3)
ANSWER:
h'(x) = 18(x^5) + 10(x^4) -36(x^3) - 18(x^2) + 10x
--Sheinle 13:28, 17 September 2010 (CDT)
(If the internal link doesn't work: http://wiki.sjs.org/wiki/index.php/Math_3_%289.10%29_Zach%27s_Question )
If f(x)= 2x^3-2x^2+x-1 find the zeroes, max/min, point of inflection,where the function is increasing/decreasing, and where the function is concave up/down.
Answers:
Zeroes: 1 Maximum: none Minimum: none Point of Inflection: (1/3,-22/27) Increasing: (-oo,oo) Concave up:(1/3,oo) Concave down:(-oo,1/3) --Yarefeen 13:18, 17 September 2010 (CDT)
Find the interesting stuff for the following equation:
y = (x^3) + 2(x^2) - 4x + 2
ANSWERS:
zero -3.37
max (-2, 10)
min (2/3, 14/27)
point of inflection (-2/3, 142/27)
increasing (-∞, -2) (2/3, ∞)
decreasing (-2, 2/3)
concave up (-2/3, ∞)
concave down (-∞, -2/3)--Kzhu 13:15, 17 September 2010 (CDT)
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/productruledirectory/ProductRule.html
Find the first derivative of the following equation:
f(x) = (x)/(x^2-4x+5)
ANSWER: f'(x) = (-x^2+5)/(x^4-8x^3+26x^2-40x+25)--Mhansen 13:36, 17 September 2010 (CDT)
Math 3 (9.10)/Rohan's Question Rramchand 13:43, 17 September 2010 (CDT)
Find the antiderivative of (x^3)-4(x^2)+10x.
ANSWER: (1/4)x^4 - (4/3)x^3 + 5x^2
--Awang 13:46, 17 September 2010 (CDT)
http://wiki.sjs.org/wiki/index.php/Math_3_(9.10)-jcowan
Find the derivative for the product of these two functions: f(x)=4x^3-5 g(x)=x^3-3x
ANSWER: h'(x)=24x^5-48x^3-15x^2+15 --Areyes 14:12, 17 September 2010 (CDT)
Find the derivative of f(x)=(2x+1)/(3x^2-2)
ANSWER: f'(x)= (-6x^2-6x-4)/(9x^4-12x^2+4) --Alandrum 14:17, 17 September 2010 (CDT)
Find the derivative of f(x)=(x+7)/((x+1)^2) (This interesting link might help http://en.wikipedia.org/wiki/Walrus)
ANSWER: f'(x)= (-x-13)/((x+1)^3)
Why is a constant divided by zero undefined?
ANSWER:
1) Consider f(x) = 1/x. As x approaches 0 from the left, f(x) approaches negative infinity. As x approaches 0 from the right, f(x) approaches infinity. Thus, it is undefined.
2) For 0/0 -- 0 divided by a constant integer will be 0. A constant integer divided by zero will be either infinity or negative infinity. It could be 0, positive infinity, or negative infinity.
Note: These answers might be wrong. idklol --Kwong 14:14, 18 September 2010 (CDT)
Approximate f(x) near x=a using the property of local linearity. What happens as x->a? If h(x)=f(x)g(x), how would you use this method of approximation in order to come up with an accurate h’(x)?
Answers: f(x) =(approximately) f'(a)(x-a)+f(a), the approximation becomes an exact value for f(a), multiply the approximations of f(x) and g(x) completely out and take the derivative (yields the quotient rule because it isn't anything special and valid for any a). --Gbailey 19:01, 18 September 2010 (CDT)
Does (d/dx)(x^2+1)^2 = 2(x^2+1)? Prove/disprove it. What does this suggest about the Power Rule as a tool for taking derivatives?
Answer: No. (d/dx)(x^2+1)^2 = (d/dx)(x^4+2x^2+1) = 4x^3+4x. 4x^3+4x does not equal 2(x^2+1). This suggests that the Power Rule is not always reliable for taking derivatives. In fact, it is only accurate when deriving a single, fully expanded polynomial. This makes the Power Rule very unwieldy for high-degree polynomials and outright useless for other types of functions. --Pbhamidipati 00:56, 19 September 2010 (CDT)
