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Raphael Pimenta · Apr 12, 2007, 07:45 AM

My question is simple, maybe for an experts, but I don't know how to do it!

CALCULUS

y(x) = x³ - 3x² + 2x

a) Find the extremes of the function for 0 ≤ x ≤ 3

b) Sketch the function for 0 ≤ x ≤ 3

c) calculate the total area between x = 0, x = 3

DIFFERENTIATE

a) √x² - x → (The square root is for the whole equation, task a! )

b) sin(x) cos(x) - e³* → * is x!!

c) Ln (x)/x²

d) Ln (x) Tan (x)

Please if someone knows how to sort it out!!

Regards,

Raphael

Capuchin · Apr 12, 2007, 07:46 AM

Could you take out all the size tabs? Did you copy this from another forum?

galactus · Apr 12, 2007, 08:44 AM

Hello Raphael:

Surely you have an inkling of what to do. This is basic calc. Where are your troubles?

Do you have a graphing calculator? That'll help to see the max and min.

$\int_{0}^{3}[x^{3}-3x^{2}+2x]dx$

Integrate this over 0 to 3 to find the area.

When it comes to differentiating and integrating, polynomials are some of the easiest to work with because they're continuous everywhere.

For the differentiation portion, use the quotient rule and product rule.

Here's a freebie:

Differentiate ln(x)tan(x):

Product rule:

$ln(x)\cdot{\underbrace{sec^{2}(x)}_{\text{derivati ve of tan(x)}}}+tan(x)\cdot\overbrace{\frac{1}{x}}^{\tex t{derivative of ln(x)}}$