I need all calculations to be shown, and the criteria to be fulfilled. please give full details as i wlould like to try understand the answers

1. Differentiate the following with respect to ‘x’

a) y = x^4 – 3x^2 + 2

b) y = 3x – 5x^3

c) y = 6 / squareroot x – 4 squareroot x

d) y = (x+5) (2x-1)

(Criteria to meet: Differentiate from 1^{st} principle)

2. Find the gradient of the curve y = (4-x^3) / x^2 at the point (-2, 3)

(Criteria to meet: Use differentiation to find gradient, tangent and normal to a given curve)

3. Given the y = x^3 – 4x^2 + 5x – 2 find dy/dx.

“p” is a point on the curve where x=3

a) Calculate the “Y” coordinate of “p”

b) Calculate the gradient at “P”

c) Find the equation of the tangent at “P”

d) Find the equation of the normal at “P”

e) Find the values of “x” for which the curve has a gradient of 5.

(Criteria to meet: Use differentiation to find gradient, tangent and normal to a given curve)

4. A curve has the euation y = 2x^3 – 3x^2 – 36x + 120

a) Calculate the value of “y” when x=3 and x= -2

b) Find dy/dx

c) Use your expression for dy/dx to find the coordinates of the two stationary points on the curves.

d) By considering the values of dy/dx near the stationary points, decide which type of stationary point each is

e) Sketch the curve

(Criteria to meet: Find max. min. and point of inflexion , Sketch quadratic and cubic graphs).

5. Differentiate y = 2x^2 + x using the first principle

Subject | Mathematics |

Due By (Pacific Time) | 01/23/2013 07:00 pm |

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