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Find the gradient function of the functions

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Reference no: EM132588220

Assignment - Differentiation of polynomials and their applications

Q1. Find the derivative of the following equations

(i) y = x

(ii) y= 2x2

(iii) y= 4x4+3x3+5

Q2. Find the gradient function of the following functions at the points given

(i) y= 3x4+ 4x +5 x=2

(ii) (x2-1)2/x+1 x=1

Q3. The equation of a curve is given by y= x3+3x2-3x

(i) Find the value of y when x=1.

(ii) Find the equation of the tangent to the curve at the point x=1.

(iii) Find the equation of the normal to the curve at the point x=1.

Q4. The equation of a curve is y=2x3+3x2

(i) Find the x-intercept of the curve.

(ii) The y-intercept of the curve.

(iii) Determine stationary points and define their nature.

Q5. A closed cylinder metal tin has a radius r and height h. The capacity of the tin is 500π litres.

(i) Derive the equation of surface area in terms of radius only.

(ii) Find the value of r for which the surface area is minimum.

(iii) Calculate surface area of the metal used to make the cylinder.

Q6. The displacement of a particle S metres, t seconds after passing a fixed-point O is given by S = 3+20t-5t2. Calculate

(i) The displacement of the particle after 2 seconds.

(ii) Time taken for the particle to return to O.

(iii) Initial velocity.

(iv) Determine velocity after 1 second.

Reference no: EM132588220

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