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Given the function y=(x+1)(x-2)^2 find i) dy/dx ii) Stationary points and determine their nature

Here we have a function made from the product of two functions, so we canuse the product differenciation rule. y=uv => dy/dx=udv/dx + vdu/dx Therefore dy/dy=(x-2)^2 + 2(x-2)(x+1) Stationary points occur w...
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Answered by Russell B. • Maths tutor
5661 Views

Solve algebraically: 6a+b = 16 and 5a - 2b = 19

6a + b = 16 (1) 5a - 2b = 19 (2) (1) x 2: 12a + 2b =32 (1) + (2): 12a + 2b + 5a - 2b = 32 + 19 = 51 17a = 51 a = 51 / 17 = 3 Substitue a = 3 back into (1): (6 x 3) + b = 16 18 + b = 16 b = 16 - 18 = - 2 Subs...
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Answered by Niva R. • Maths tutor
3589 Views

Find the general solution to the differential equation '' (x^2 + 3x - 1) dy/dx = (2x + 3)y ''

Now although this might seem like quite a complex question at first, it's a little less intimidating when we take a while to look at it- you might notice that we can seperate x and y terms like so: 1/y dy = ...
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Answered by Sam T. • Maths tutor
8008 Views

Solve 0=X^2 +5x +4

0= (x + 4)(x + 1) x= - 4 x= - 1
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Answered by Rebecca W. • Maths tutor
3285 Views

Differentiate y = lnx + 4x^2 + 3e^4x with respect to x

lnx differentiates to 1/x 4x^2 differentiates to 8x 3e^4x differentiates to 12e^4x therefore the answer is: 1/x + 8x + 12e^4x
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Answered by Dhylon S. • Maths tutor
4541 Views