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Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.

Differentiation => 4X 3 - 20X 2 + 4XTo find the stationary points, set this differentiation = 04x (x 2 - 5x +4)4x (x-4)(x-1)x=0, x=4, x=1 are stationary points. Find the second derivative 12X 2 -40X +4. S...
AH
Answered by Alice H. • Maths tutor
3769 Views

Find the general solution to f''(x)+ 3f'(x)+ 2f(x)=0

Firstly, I haven't seen the notation I used in alevel but I just used it for the sake of ease of typing it online.1st. Sub in the trial solution f(x)= Ae^(mx) and its derivatives- f'(x)= Ame^(mx) and f''(x)=...
JD
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A ball is released on a smooth ramp at a distance of 5 metres from the ground. Calculate its speed when it reaches the bottom of the ramp.

The ramp is smooth, so the effects of friction can be ignored. Therefore, the potential energy lost by the ball is equivalent to the kinetic energy gained by the ball. The formula for kinetic energy is 1/2 *...
CB
Answered by Cameron B. • Maths tutor
5376 Views

'Disappointment with earthly existence is often contrasted with God's love and the rewards of Heaven'. In light of this view, consider the ways in which Christina Rossetti explores the nature of religious experience and belief in her poetry.

In the poem 'Up-Hill', it is never explicitly mentioned that this "road up-hill" is to Heaven, but the presence of an anonymous voice, answering all of the speaker's questions, certainly has an ang...
HM
6806 Views

Describe how a vaccine results in the production of antibodies against a disease causing organism.

The vaccine contains parts of the pathogen that are recognised by the immune system, these are called antigens. The antigen is recognised by innate immune cells such as macrophages that will engulf the patho...
AC
Answered by Anna C. • Biology tutor
2862 Views