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Given that the equation of the curve y=f(x) passes through the point (-1,0), find f(x) when f'(x)= 12x^2 - 8x +1

Firstly, Integrate the f'(x) equation by raising the power by 1 and then dividing by the new power and adding a constant c. This gives you f(x)=(12x^3)/3 -(8x^2)/2 + x + c Then you simplify, f(x)=4x^3 -4x^2 ...
DM
Answered by Daniel M. • Maths tutor
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If f(x)= ( ((x^2) +4)(x-3))/2x find f'(x)

Tackle differentiation questions in two parts: First put it into the simplest for possible for differenciation, then perform the differenciation. So for this equation you should first expand the top brackets...
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Answered by Alex B. • Maths tutor
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Find tan(A-B) sec^2(A) - 2tan(A) = 16 && sin(B)sec^2(B) = 64cos(B)cosec^2(B)

@tan(A) = 5, tan(B) =4, tan(A - B) = 1/21 @tan(A) = -3, tan(B) = 4, tan(A - B) = 7/11 I can demonstrate how the answers can be obtained during the session.
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Answered by Fedor S. • Maths tutor
3760 Views

Differentiate with respect to x y=(x^3)ln2x

To be able to differentiate this we need to use the product rule as we want to differentiate two functions multiplied together. The product rule states that if y=uv, then : dy/dx= u dv/dx + v du/dx. Let u= x...
JP
Answered by Jennifer P. • Maths tutor
12881 Views

The number of bacteria present in a culture at time t hours is modeled by the continuous variable N and the relationship N = 2000e^kt, where k is a constant. Given that when t = 3, N = 18 000, find (a) the value of k to 3 significant figures

putting in the conditions: 18000 = 2000e^3k .. ln(9) = 3k .. k=(1/3)ln(9)
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Answered by Benjamin C. • Maths tutor
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