Additional Mathematics Week 1

Differentiation

Given that  $y=\frac{3}{4}{\mathrm{x^2}}^{}$ , find the approximate change in x which will cause y to decrease from 48 to 47.7.

Solution:

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Given that $y=15x+\frac{24}{{\mathrm{x^3}}^{}}$ ,

(a) Find the value of when x = 2,

(b) Express in terms of k, the approximate change in y when x changes from 2 to

      2 + k, where k is a small change.

Solution:
(a)

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(b)

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If the radius of a circle increases from 4 cm to 4.01 cm, find the approximate increase in the area.

Solution:

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Given that y =3t + 5t² and x = 5t –1.

(a) Find $\frac{dy}{dx}$  in terms of x,

(b) If x increases from 5 to 5.01, find the small increase in t.

Solution:

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(a)

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(b)

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