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Given the function y = x^5 + x^3/2 + x + 7 Express the following in their simplest forms: i) dy/dx ii) ∫ y dx

i) 5x^4 + 3/2x^1/2 + 1ii) 1/6x^6 + 2/5x^5/2 + 1/2x^2 + 7x + c
LB
Answered by Liam B. • Maths tutor
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How do I know if a curve is convex?

The second differential of the equation of the curve will be positive if it is convex. This is because, by definition, convex means that the gradient of a curve is increasing. To find the gradient of a curve...
JW
Answered by Josh W. • Maths tutor
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Solve the simultaneous equations: y + 4x + 1 = 0, and y^2 + 5x^2 + 2x = 0.

"Solve the simultaneous equations" is another way of saying find the unknown variables. In this case, they are x and y. When looking at the second equation, y^2+5x^2+2x=0, we can see that we have t...
Answered by • Maths tutor
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Given that the graph f(x) passes through the point (2,3) and that f'(x)=6x^2-14x+3, find f(x).

For this question we already have the derivative of f(x), and so if we integrate it we should get to a general equation with a constant on the end, however we want to get to an exact solution which we should...
Answered by • Maths tutor
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Find the surface area of a hand held fan (modeled with negligible depth) with radius 8 cm and a 60 degree angle at the centre

60 degrees = π/3 radians A = 1/2r 2 θr = 8θ = π/3 1/2 x 8 2 x π/3 = 33.5103216... cm 2 33.5103216... x 2 = 67.0 cm 2 to 3 s.f.
Answered by • Maths tutor
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