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My exact explanation would depend on the students level of understanding. The following answer assumes a basic understanding of differentiation and equations of lines; a) Gradient of tangent is equal to g...
To differentiate xx, we first let y = xx. (Note that xx is not in the form xc w...
The main piece of information this question gives us is that the two lines do not cross or touch. From this we can immediately see that we will need to use the discriminant of the quadratic formula b...
In order to solve this question we simply must substitute x=1 into f(x).
If we carry out this substitution we see that
f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1 - 5 + c...
sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1
(sin^2(x) + cos^2(x) =1) Therefore;
1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1
Cancelling out on b...
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