how to solve 2

Question

1. Expand (3x+6)^0.5 to four terms only. 2. Given: y=[(sin 3x)/(4x^3)] Differentiate by using the quotient rule. 3. Given: y=x^3 - 6x^2 + 11x - 6 Calculate with the aid of differentiation, the co-ordinates of the turning points and the point of inflection. 4. Differentiate the following with respect to x: y=-3e^(-2x) - [log (e below the log) 1/x^3] - cosec 3x + (pie.p) + 7x^3

Answer 1

(3).

The function is .

At turning points  or  does not exist.

Find the first derivative with respect to x.

Compare the equation with the general form of quadratic equation .

.

Substitute in the quadratic formula : .

If x = 2.6 then

If x = 1.4 then .

The turning points are .

At points of inflection or does not exist.

Find the second derivative with respect to x.

If x = 2 then .

The point of inflection is .

Answer 2

(2).

The function is .

Differentiate with respect to x.

Apply quotient rule:

Answer 3

(4).

The function is .

Differentiate with respect to x.

Answer 4

(1).

The expression is (3x + 6)^0.5.

The related function is

The Maclaurin series for f(x)